## Elementary Algebra

{$0,1$}
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 {$0,1$}.