24y^2=-9y

Solution for 24y^2=-9y equation:

Simplifying
24y2 = -9y

Solving
24y2 = -9y

Solving for variable 'y'.

Reorder the terms:
9y + 24y2 = -9y + 9y

Combine like terms: -9y + 9y = 0
9y + 24y2 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(3 + 8y) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0
Subproblem 2
Set the factor '(3 + 8y)' equal to zero and attempt to solve:

Simplifying
3 + 8y = 0

Solving
3 + 8y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 8y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8y = 0 + -3
8y = 0 + -3

Combine like terms: 0 + -3 = -3
8y = -3

Divide each side by '8'.
y = -0.375

Simplifying
y = -0.375
Solution
y = {0, -0.375}