document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852178>Question 852178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5x^3+30x^2-15x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513211 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=513211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to solve for x, the first thing you want to do is set this expression equal to 0:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E3%2B30x%5E2-15x=0 ALIGN=MIDDLE  ALT=\"5x%5E3%2B30x%5E2-15x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, since each of these terms have 5x in common, we can factor 5x out of the equation, giving us:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%28x%5E2%2B6x-3%29=0 ALIGN=MIDDLE  ALT=\"5x%28x%5E2%2B6x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Setting each of these terms equal to 0, gives us:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=0 ALIGN=MIDDLE  ALT=\"5x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With 5x = 0, we can quickly see that x = 0, so, we know that one of the values of x is 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, in order to find the other two values of x, we need to use the quadratic formula on our second term, x^2 + 6x - 3 = 0:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+36%2B12+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36%2B12+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+48+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+48+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+4%2Asqrt%28+3+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+4%2Asqrt%28+3+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, we can factor a 2 out of the numerator, since 2 is a factor of both -6 and +- 4:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282%28-3+%2B-+2%2Asqrt%28+3+%29%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%282%28-3+%2B-+2%2Asqrt%28+3+%29%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3+%2B-+2%2Asqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"x+=+-3+%2B-+2%2Asqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now have our 3 values of x: 0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2B2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-3%2B2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"-3-2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );