S^3-S=0

Solution for S^3-S=0 equation:

Simplifying
S3 + -1S = 0

Reorder the terms:
-1S + S3 = 0

Solving
-1S + S3 = 0

Solving for variable 'S'.

Factor out the Greatest Common Factor (GCF), 'S'.
S(-1 + S2) = 0

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

Subproblem 1
Set the factor 'S' equal to zero and attempt to solve:

Simplifying
S = 0

Solving
S = 0

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

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

Simplifying
1 + S = 0

Solving
1 + S = 0

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

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

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

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

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

Simplifying
-1 + S = 0

Solving
-1 + S = 0

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

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

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

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

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