Solve for y 6y^2=-30y

$6 y^{2} = - 30 y$

Add $30 y$ to both sides of the equation.

$6 y^{2} + 30 y = 0$

Factor $6 y$ out of $6 y^{2} + 30 y$ .

Factor $6 y$ out of $6 y^{2}$ .

$6 y (y) + 30 y = 0$

Factor $6 y$ out of $30 y$ .

$6 y (y) + 6 y (5) = 0$

Factor $6 y$ out of $6 y (y) + 6 y (5)$ .

$6 y (y + 5) = 0$

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

$y = 0$

$y + 5 = 0$

Set $y$ equal to $0$ .

$y = 0$

Set $y + 5$ equal to $0$ and solve for $y$ .

Set $y + 5$ equal to $0$ .

$y + 5 = 0$

Subtract $5$ from both sides of the equation.

$y = - 5$

The final solution is all the values that make $6 y (y + 5) = 0$ true.

$y = 0, - 5$