Find the Roots (Zeros) x^2+x

$x^{2} + x$

Set $x^{2} + x$ equal to $0$ .

$x^{2} + x = 0$

Solve for $x$ .

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

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

$x \cdot x + x = 0$

Raise $x$ to the power of $1$ .

$x \cdot x + x = 0$

Factor $x$ out of $x^{1}$ .

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

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 $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$x = 0, - 1$