Solve for w w^2=-12w

$w^{2} = - 12 w$

Add $12 w$ to both sides of the equation.

$w^{2} + 12 w = 0$

Factor $w$ out of $w^{2} + 12 w$ .

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

$w \cdot w + 12 w = 0$

Factor $w$ out of $12 w$ .

$w \cdot w + w \cdot 12 = 0$

Factor $w$ out of $w \cdot w + w \cdot 12$ .

$w (w + 12) = 0$

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

$w = 0$

$w + 12 = 0$

Set $w$ equal to $0$ .

$w = 0$

Set $w + 12$ equal to $0$ and solve for $w$ .

Set $w + 12$ equal to $0$ .

$w + 12 = 0$

Subtract $12$ from both sides of the equation.

$w = - 12$

The final solution is all the values that make $w (w + 12) = 0$ true.

$w = 0, - 12$