document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009206>Question 1009206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve equations by factoring?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624746 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=624746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The most fundamental tools for solving equations are addition, subtraction, multiplication, and division. These methods work well for equations like: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2+=+10+-+2x+ ALIGN=MIDDLE  ALT=\"x+%2B+2+=+10+-+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"2%28x+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But what about equations where the variable carries an exponent, like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+=+8x+-+6 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+=+8x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >? This is where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=factoring ALIGN=MIDDLE  ALT=\"factoring\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes in. \r<BR>\n" );
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document.write( "The Solve by Factoring process will require four major steps:\r<BR>\n" );
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document.write( "        Move all terms to one side of the equation, usually the left, using addition or subtraction.<BR>\n" );
document.write( "        Factor the equation completely.<BR>\n" );
document.write( "        Set each factor equal to zero, and solve.<BR>\n" );
document.write( "        List each solution from Step 3 as a solution to the original equation.\r<BR>\n" );
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document.write( " Example:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+=+8x+-+6+ ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+=+8x+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1\r<BR>\n" );
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document.write( "The first step is to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=move ALIGN=MIDDLE  ALT=\"move\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+all ALIGN=MIDDLE  ALT=\"+all\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+terms ALIGN=MIDDLE  ALT=\"+terms\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=left ALIGN=MIDDLE  ALT=\"left\"   DISABLED_style= \"max-width:90%; height:auto;\" > using addition and subtraction. First, we will subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x ALIGN=MIDDLE  ALT=\"8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from each side.\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+3x+-+8x+=+8x+-+8x+-+6 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+3x+-+8x+=+8x+-+8x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+=+-6+ ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+=+-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we will add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to each side.\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+%2B+6+=+-6+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+%2B+6+=+-6+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "With all terms on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=left ALIGN=MIDDLE  ALT=\"left\"   DISABLED_style= \"max-width:90%; height:auto;\" > side, we proceed to\r<BR>\n" );
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document.write( "Step 2\r<BR>\n" );
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document.write( "We identify the left as a trinomial, and factor it accordingly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5x+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x ALIGN=MIDDLE  ALT=\"-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-3x ALIGN=MIDDLE  ALT=\"-2x-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x+-3x%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+-3x%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+2x%29+-%283x-+6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+2x%29+-%283x-+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x+-+2%29+-3%28x-+2%29+=+0 ALIGN=MIDDLE  ALT=\"x%28x+-+2%29+-3%28x-+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+-+2%29%28x+-+3%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x+-+2%29%28x+-+3%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We now have two factors, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29+ ALIGN=MIDDLE  ALT=\"%28x+-+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29 ALIGN=MIDDLE  ALT=\"%28x+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Step 3\r<BR>\n" );
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document.write( "We now set each factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The result is two subproblems:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+++x+-+2+=+0+ ALIGN=MIDDLE  ALT=\"+++x+-+2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3+=+0+ ALIGN=MIDDLE  ALT=\"x+-+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving the first subproblem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2+=+0 ALIGN=MIDDLE  ALT=\"x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Solving the second subproblem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3+=+0 ALIGN=MIDDLE  ALT=\"x+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Step 4\r<BR>\n" );
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document.write( "The final step is to combine the two previous solutions, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, into one solution for the original problem.\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+=+8x+-+6 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+=+8x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+ ALIGN=MIDDLE  ALT=\"+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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