y^3=(-6y)

Solution for y^3=(-6y) equation:

Simplifying
y3 = (-6y)

Solving
y3 = (-6y)

Solving for variable 'y'.

Reorder the terms:
(6y) + y3 = (-6y) + (6y)

Combine like terms: (-6y) + (6y) = 0
(6y) + y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(6 + y2) = 0

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 '(6 + y2)' equal to zero and attempt to solve:

Simplifying
6 + y2 = 0

Solving
6 + y2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y2 = 0 + -6
y2 = 0 + -6

Combine like terms: 0 + -6 = -6
y2 = -6

Simplifying
y2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}