2y^3+6y=0

Solution for 2y^3+6y=0 equation:

Simplifying
2y3 + 6y = 0

Reorder the terms:
6y + 2y3 = 0

Solving
6y + 2y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(3 + y2) = 0

Ignore the factor 2.
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 + y2)' equal to zero and attempt to solve:

Simplifying
3 + y2 = 0

Solving
3 + y2 = 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 + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y2 = 0 + -3
y2 = 0 + -3

Combine like terms: 0 + -3 = -3
y2 = -3

Simplifying
y2 = -3

The solution to this equation could not be determined.

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