document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80874>Question 80874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the equation\r<BR>\n" );
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document.write( "(3w+4)(2w-7)=0<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 #58034 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=58034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the equation:<BR>\n" );
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document.write( "(3w+4)(2w-7)=0<BR>\n" );
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document.write( "Solve for w.<BR>\n" );
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document.write( "Notice that if at least one of the two factors on the left side of the equation is zero, then<BR>\n" );
document.write( "the equation will be true because zero times anything is zero.<BR>\n" );
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document.write( "Therefore, the equation will be true if either 3w + 4 = 0 or if 2w - 7 = 0 because that will<BR>\n" );
document.write( "make the left side equal the right side.<BR>\n" );
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document.write( "Let's first say that (3w + 4) equals zero. <BR>\n" );
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document.write( "3w + 4 = 0 <BR>\n" );
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document.write( "Solve for w by first subtracting 4 from both sides to get:<BR>\n" );
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document.write( "3w = -4<BR>\n" );
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document.write( "Then divide both sides by 3 (which is the multiplier of w) to get:<BR>\n" );
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document.write( "w = -4/3<BR>\n" );
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document.write( "So that's one value for w that will make the equation true.<BR>\n" );
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document.write( "Next let's look at the second factor ... (2w - 7) and set it equal to zero:<BR>\n" );
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document.write( "2w - 7 = 0<BR>\n" );
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document.write( "Get rid of the -7 on the left side by adding 7 to both sides to get:<BR>\n" );
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document.write( "2w = 7<BR>\n" );
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document.write( "Solve for w by dividing both sides by 2 and the result is:<BR>\n" );
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document.write( "w = 7/2<BR>\n" );
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document.write( "That's the second value for w that will make the equation true.<BR>\n" );
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document.write( "In summary, the values of w that will make the equation true are:<BR>\n" );
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document.write( "w = -4/3 and<BR>\n" );
document.write( "w = 7/2<BR>\n" );
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document.write( "Hope this helps you to understand why setting each of the factors equal to zero will give<BR>\n" );
document.write( "you two values for w that make the equation work.<BR>\n" );
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