document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049044>Question 1049044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve equation\r<BR>\n" );
document.write( "\n" );
document.write( "3x^3+19x^2-72x=0\r<BR>\n" );
document.write( "\n" );
document.write( "please show steps </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664638 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=664638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rational Roots Theorem will give several roots to check using Synthetic Division.  Each root found narrows which roots still need to be found.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72=2%2A36=2%2A6%2A6=2%2A2%2A3%2A6%2A2%2A2%2A3%2A2%2A3=12%2A6 ALIGN=MIDDLE  ALT=\"72=2%2A36=2%2A6%2A6=2%2A2%2A3%2A6%2A2%2A2%2A3%2A2%2A3=12%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "Try to make a list of all combinations of factors for 72.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2872=these%2C2%2A36%2C3%2A24%2C4%2A18%2C6%2A12%2C8%2A9%29 ALIGN=MIDDLE  ALT=\"system%2872=these%2C2%2A36%2C3%2A24%2C4%2A18%2C6%2A12%2C8%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Making a full complete list still takes more work because of division by 3 from the leading term.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Try the PLUSes and MINUSES of 2, 3, 4, 6, 8, 9, 12, 18.<BR>\n" );
document.write( "The dividend to use should include all degrees of x less than and equal to 3.... No, not really....  <BR>\n" );
document.write( "Why?<BR>\n" );
document.write( "Because you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283x%5E2%2B19x-72%29=0 ALIGN=MIDDLE  ALT=\"x%283x%5E2%2B19x-72%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You will NOT REALLY NEED Rational Roots Theorem because you have a function of x multiplied by a quadratic in x.  JUST FIND THE ZEROS OF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283x%5E2%2B19x-72%29 ALIGN=MIDDLE  ALT=\"highlight_green%283x%5E2%2B19x-72%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; you already know that one of your zeros or roots will be x=0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Roots from the quadratic factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-19%2B-+sqrt%2819%5E2%2B4%2A3%2A72%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-19%2B-+sqrt%2819%5E2%2B4%2A3%2A72%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-19%2B-+sqrt%281225%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-19%2B-+sqrt%281225%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-19%2B-+35%29%2F2 ALIGN=MIDDLE  ALT=\"%28-19%2B-+35%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<b>-27 and  8</b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "The three solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-27%2C0%2C8%29 ALIGN=MIDDLE  ALT=\"system%28-27%2C0%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "-------------------------------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );