document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=420033>Question 420033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find the real number solutions of this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18x%5E3=50x+ ALIGN=MIDDLE  ALT=\"+18x%5E3=50x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293602 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=293602\">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=18x%5E3=50x ALIGN=MIDDLE  ALT=\"18x%5E3=50x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In general, to solve equations where the variable has exponents larger than 1, you:<ul><li>Get one side of the equation to be zero.</li><li>Factor the the other side.</li><li>Use the Zero Product Property.</li><li>Solve the equations from the Zero Product Property.</ul><BR>\n" );
document.write( "So we start by subtracting 50x from each side:<BR>\n" );
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document.write( "Now we factor. And factoring always starts with the Greatest Common Factor (GCF). The GCF is 2x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%289x%5E2-25%29+=+0 ALIGN=MIDDLE  ALT=\"2x%289x%5E2-25%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The second factor is a difference of squares so it will factor according to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern:<BR>\n" );
document.write( "2x(3x+5)(3x-5) = 0<BR>\n" );
document.write( "We are finished factoring. The Zero Product Property tells us this (or any) product can be zero only if one (or more) of the factors is zero. So:<BR>\n" );
document.write( "2x = 0 or 3x+5 = 0 or 3x-5 = 0<BR>\n" );
document.write( "Solving each of these we get:<BR>\n" );
document.write( "x = 0 or x = -5/3 or x = 5/3<BR>\n" );
document.write( "These are the three real solutions to your equation.<br><BR>\n" );
document.write( "P.S. \"Exponential equations\" are equations where the variable is in the exponent. Your equation is what is called a \"Polynomial equation\". Posting your problems under the right category may result in faster responses from the tutors. </SPAN>\n" );
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