document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112542>Question 112542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (ax+b)(2x-3)=18x^2-23x+c, find the values of a, b, and c.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82083 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82083\">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=%28ax%2Bb%29%282x-3%29=18x%5E2-23x%2Bc ALIGN=MIDDLE  ALT=\"%28ax%2Bb%29%282x-3%29=18x%5E2-23x%2Bc\"   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=2ax%5E2-3ax%2B2bx-3b=18x%5E2-23x%2Bc ALIGN=MIDDLE  ALT=\"2ax%5E2-3ax%2B2bx-3b=18x%5E2-23x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ax%5E2%2B%28-3a%2B2b%29x-3b=18x%5E2-23x%2Bc ALIGN=MIDDLE  ALT=\"2ax%5E2%2B%28-3a%2B2b%29x-3b=18x%5E2-23x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we can extract some facts:\r<BR>\n" );
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document.write( "Fact 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=18 ALIGN=MIDDLE  ALT=\"2a=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Because the leading coefficients must be equal<BR>\n" );
document.write( "Fact 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3a%2B2b=-23 ALIGN=MIDDLE  ALT=\"-3a%2B2b=-23\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Because the first degree term coefficients must be equal<BR>\n" );
document.write( "Fact 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3b=c ALIGN=MIDDLE  ALT=\"-3b=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Because the constant coefficients must be equal\r<BR>\n" );
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document.write( "Solving the Fact 1 equation for a gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9 ALIGN=MIDDLE  ALT=\"a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We can use this value to solve the Fact 2 equation, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%289%29%2B2b=-23 ALIGN=MIDDLE  ALT=\"-3%289%29%2B2b=-23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=-23%2B27 ALIGN=MIDDLE  ALT=\"2b=-23%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=4 ALIGN=MIDDLE  ALT=\"2b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And then using our newly found value for b, we can solve the last equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%282%29=c ALIGN=MIDDLE  ALT=\"-3%282%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-6 ALIGN=MIDDLE  ALT=\"c=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%2B2%29%282x-3%29=18x%5E2-23x-6 ALIGN=MIDDLE  ALT=\"%289x%2B2%29%282x-3%29=18x%5E2-23x-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=%289x%2B2%29%282x-3%29 ALIGN=MIDDLE  ALT=\"%289x%2B2%29%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%5E2-27x%2B4x-6 ALIGN=MIDDLE  ALT=\"18x%5E2-27x%2B4x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%5E2-23x-6 ALIGN=MIDDLE  ALT=\"18x%5E2-23x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Check!\r<BR>\n" );
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document.write( "Hope this helps. </SPAN>\n" );
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