4y^3-2y=

Solution for 4y^3-2y= 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

Take the square root of each side:
y = {-0.707106781, 0.707106781}
Solution
y = {0, -0.707106781, 0.707106781}