document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211912>Question 211912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you figure out this problem: -5x(2x-1)=3(x+4)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160094 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you figure out this problem: -5x(2x-1)=3(x+4) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1. Multiply everything out on both sides of the equation. After we mess around with the equation, we will get a quadratic equation.  Here it goes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     -5x(2x-1)=3(x+4) will yield:  -10x^2+5x=3x+12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Now let's put everything on the right side so that the left side is zero.  I like a positive number for the x^2 term.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   Step 2a.  Add 10x^2 to both sides of equation in Step 1:  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     10x^2-10x^2+5x=10x^2+3x+12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note:  The 10x^2 terms cancel out on the left side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  Step 2b.  Simplify equation in step 2a. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     5x=10x^2+3x+12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Subtract 5x both sides of equation in Step 2b to make left side =0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     5x-5x=10x^2+3x-12-5x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note:  Collect like terms and simplify 3x-5x=-2x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   Step 3a. Simplify to yield our final equation \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     0=10x^2-2x-12 OR 10x^2-2x-12=0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Now we have a quadratic equation in step 3a.\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( "where a=10, b=-2, and c=-12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Substitute a, b, and c in the formula.  The steps are shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note when the quadratic equation is a parabola when the values of x are real numbers.  See graph where it intersects the x-axis.  This is when y=0, hence our quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-2x%2B-12+=+0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-2x%2B-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-2%29%5E2-4%2A10%2A-12=484 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A10%2A-12=484\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=484 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--2%2B-sqrt%28+484+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+484+%29%29%2F2%5Ca\"   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=x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+484+%29%29%2F2%5C10+=+1.2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+484+%29%29%2F2%5C10+=+1.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-2%29-sqrt%28+484+%29%29%2F2%5C10+=+-1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+484+%29%29%2F2%5C10+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-2x%2B-12 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-2x%2B-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-2x%2B-12+=+10%28x-1.2%29%2A%28x--1%29 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-2x%2B-12+=+10%28x-1.2%29%2A%28x--1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.2, -1.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-2%2Ax%2B-12+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-2%2Ax%2B-12+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra \r<BR>\n" );
document.write( "\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );