Solve for y 5y^2=-10y

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

Step 1

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

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

Step 2

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

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

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

Factor $5 y$ out of $10 y$ .

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

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

$5 y (y + 2) = 0$

Step 3

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

$y = 0$

$y + 2 = 0$

Step 4

Set $y$ equal to $0$ .

$y = 0$

Step 5

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

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

$y + 2 = 0$

Subtract $2$ from both sides of the equation.

$y = - 2$

Step 6

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

$y = 0, - 2$