Question 55167
solve {{{6x^2-2=x}}} by factoring.
First put the equation in standard form {{{highlight(ax^2+bx+c=0)}}}
{{{6x^2-x-2=x-x}}}
{{{6x^2-x-2=0}}}
a=6, b=-1, and c=-2
We need to replace b (-1) with two integers that when multiplied give you a*c=6*-2=-12.
-4*3=-12
-4+3=-1
{{{6x^2-4x+3x-2=0}}} Factor by grouping.
{{{(6x^2-4x)+(3x-2)=0}}}
{{{2x(3x-2)+1(3x-2)=0}}}
{{{(2x+1)(3x-2)=0}}}  Set each parenthesis = to 0 and solve for x.
{{{2x+1=0}}} and {{{3x-2=0}}}
{{{2x+1-1=0-1}}} and {{{3x-2+2=0+2}}}
{{{2x=-1}}} and {{{3x=2}}}
{{{2x/2=-1/2}}} and {{{3x/3=2/3}}}
{{{x=-1/2}}} and {{{x=2/3}}}
Another way to write it is x={-1/2,2/3}
Happy Calculating!!!