Solve for w 5w^2=-10w

$5 w^{2} = - 10 w$

Add $10 w$ to both sides of the equation.

$5 w^{2} + 10 w = 0$

Factor $5 w$ out of $5 w^{2} + 10 w$ .

Factor $5 w$ out of $5 w^{2}$ .

$5 w (w) + 10 w = 0$

Factor $5 w$ out of $10 w$ .

$5 w (w) + 5 w (2) = 0$

Factor $5 w$ out of $5 w (w) + 5 w (2)$ .

$5 w (w + 2) = 0$

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

$w = 0$

$w + 2 = 0$

Set $w$ equal to $0$ .

$w = 0$

Set $w + 2$ equal to $0$ and solve for $w$ .

Set $w + 2$ equal to $0$ .

$w + 2 = 0$

Subtract $2$ from both sides of the equation.

$w = - 2$

The final solution is all the values that make $5 w (w + 2) = 0$ true.

$w = 0, - 2$