2Y^3-2Y=0

Solution for 2Y^3-2Y=0 equation:

Simplifying
2Y3 + -2Y = 0

Reorder the terms:
-2Y + 2Y3 = 0

Solving
-2Y + 2Y3 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '2Y'.
2Y(-1 + Y2) = 0

Factor a difference between two squares.
2Y((1 + Y)(-1 + Y)) = 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 + Y)' equal to zero and attempt to solve:

Simplifying
1 + Y = 0

Solving
1 + Y = 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 + Y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + Y = 0 + -1
Y = 0 + -1

Combine like terms: 0 + -1 = -1
Y = -1

Simplifying
Y = -1
Subproblem 3
Set the factor '(-1 + Y)' equal to zero and attempt to solve:

Simplifying
-1 + Y = 0

Solving
-1 + Y = 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 + Y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + Y = 0 + 1
Y = 0 + 1

Combine like terms: 0 + 1 = 1
Y = 1

Simplifying
Y = 1
Solution
Y = {0, -1, 1}