Solve by Factoring x^2=x

$x^{2} = x$

Subtract $x$ from both sides of the equation.

$x^{2} - x = 0$

Factor $x$ out of $x^{2} - x$ .

Factor $x$ out of $x^{2}$ .

$x \cdot x - x = 0$

Factor $x$ out of $- x$ .

$x \cdot x + x \cdot - 1 = 0$

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

$x (x - 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x - 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $x (x - 1) = 0$ true.

$x = 0, 1$