Solve for a a^2+a=0

$a^{2} + a = 0$

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

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

$a \cdot a + a = 0$

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

$a \cdot a + a = 0$

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

$a \cdot a + a \cdot 1 = 0$

Factor $a$ out of $a \cdot a + a \cdot 1$ .

$a (a + 1) = 0$

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

$a = 0$

$a + 1 = 0$

Set $a$ equal to $0$ .

$a = 0$

Set $a + 1$ equal to $0$ and solve for $a$ .

Set $a + 1$ equal to $0$ .

$a + 1 = 0$

Subtract $1$ from both sides of the equation.

$a = - 1$

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

$a = 0, - 1$