9y(y^2-9)=0

Solution for 9y(y^2-9)=0 equation:

Simplifying
9y(y2 + -9) = 0

Reorder the terms:
9y(-9 + y2) = 0
(-9 * 9y + y2 * 9y) = 0
(-81y + 9y3) = 0

Solving
-81y + 9y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9y'.
9y(-9 + y2) = 0

Factor a difference between two squares.
9y((3 + y)(-3 + y)) = 0

Ignore the factor 9.
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 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

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

Simplifying
-3 + y = 0

Solving
-3 + y = 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 + y = 0 + 3

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

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

Simplifying
y = 3
Solution
y = {0, -3, 3}