Answer
{$0,1$}
Work Step by Step
We rearrange the equation into the standard form of a quadratic equation and factor out $x$. We then equate both the factors to zero and solve the equation:
$x^{2}=x$
$x^{2}-x+0=0$
$x^{2}-x=0$
$x(x-1)=0$
$x=0$ and $(x-1)=0$
$x=0$ and $x=1$
Therefore, the solution set is {$0,1$}.
