document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72957>Question 72957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> m^3+2m^2-3m=0  Solve each equation so Far i have \r<BR>\n" );
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document.write( "M(M^2+2m-3)=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52183 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A%28m%5E2%2B2m-3=0 ALIGN=MIDDLE  ALT=\"m%2A%28m%5E2%2B2m-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So far you are correct.<BR>\n" );
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document.write( "The next thing you can do is notice that the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+%2B+2m+-3 ALIGN=MIDDLE  ALT=\"m%5E2+%2B+2m+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored. It<BR>\n" );
document.write( "factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m+%2B+3%29%2A%28m+-+1%29 ALIGN=MIDDLE  ALT=\"%28m+%2B+3%29%2A%28m+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Now you can return to your equation and substitute these factors for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+%2B+2m+-3 ALIGN=MIDDLE  ALT=\"m%5E2+%2B+2m+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "you will then have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2A%28m%2B3%29%2A%28m-1%29+=+0 ALIGN=MIDDLE  ALT=\"m%2A%28m%2B3%29%2A%28m-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that this equation will be true if any of the factors on the left side equals zero.<BR>\n" );
document.write( "This is because a zero factor on the left side is a multiplier and it will make the whole<BR>\n" );
document.write( "left side equal to zero which is also the right side.  Therefore, with a zero factor the<BR>\n" );
document.write( "equation is balanced because 0 equals 0 is the result.<BR>\n" );
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document.write( "So all you have to do is set each of the three factors equal to zero and solve for m.<BR>\n" );
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document.write( "The first factor is m and setting it equal to zero says: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+0 ALIGN=MIDDLE  ALT=\"m+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This becomes one<BR>\n" );
document.write( "of the answers.<BR>\n" );
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document.write( "The second factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+%2B+3 ALIGN=MIDDLE  ALT=\"m+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and setting it equal to zero results in: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"m+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You<BR>\n" );
document.write( "can solve for m by subtracting +3 from both sides to get rid of the +3 on the left side.<BR>\n" );
document.write( "When you subtract +3 from both sides you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-3 ALIGN=MIDDLE  ALT=\"m+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that is the second answer.<BR>\n" );
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document.write( "Finally, the third factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+-+1 ALIGN=MIDDLE  ALT=\"m+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and setting it equal to zero gives you the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+-+1+=+0 ALIGN=MIDDLE  ALT=\"m+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You can solve this equation for m by adding 1 to both sides to eliminate the<BR>\n" );
document.write( "-1 on the left side.  Adding +1 to both sides of this equation results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2B1 ALIGN=MIDDLE  ALT=\"m+=+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So the three possible answers for m are 0, -3, and +1.  Each of these three can be substituted<BR>\n" );
document.write( "back into the original equation given in the problem, and that equation will become<BR>\n" );
document.write( "equal on both sides.<BR>\n" );
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document.write( "I hope this helps you understand the problem a little more.  The hardest part of this problem<BR>\n" );
document.write( "was to recognize that you could factor the quadratic terms and then to find the factors. It<BR>\n" );
document.write( "takes a lot of practice to do this and you are well on your way to getting it.  Keep up the<BR>\n" );
document.write( "good work! </SPAN>\n" );
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