2q^3-2q=0

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

Simplifying
2q3 + -2q = 0

Reorder the terms:
-2q + 2q3 = 0

Solving
-2q + 2q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q'.
2q(-1 + q2) = 0

Factor a difference between two squares.
2q((1 + q)(-1 + q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

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

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

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

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

Simplifying
-1 + q = 0

Solving
-1 + q = 0

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

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

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

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

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