Answer
{$1,2$}
Work Step by Step
We use the distributive property in order to put the equation into trinomial form. We then use the rules of factoring trinomials to solve the equation:
$2(x-1)-x(x-1)=0$
$2x-2-x^{2}+x=0$
$-x^{2}+x+2x-2=0$
$-x^{2}+3x-2=0$
$x^{2}-3x+2=0$
$x^{2}-1x-2x+2=0$
$x(x-1)-2(x-1)=0$
$(x-1)(x-2)=0$
$(x-1)=0$ and $(x-2)=0$
$x=1$ and $x=2$
Therefore, the solution set is {$1,2$}.
