4y^3+2y=0

Solution for 4y^3+2y=0 equation:

Simplifying
4y3 + 2y = 0

Reorder the terms:
2y + 4y3 = 0

Solving
2y + 4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(1 + 2y2) = 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 '(1 + 2y2)' equal to zero and attempt to solve:

Simplifying
1 + 2y2 = 0

Solving
1 + 2y2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y2 = 0 + -1
2y2 = 0 + -1

Combine like terms: 0 + -1 = -1
2y2 = -1

Divide each side by '2'.
y2 = -0.5

Simplifying
y2 = -0.5

The solution to this equation could not be determined.

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