# 5x^3-5x=0

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## Solution for 5x^3-5x=0 equation:

Simplifying
5x3 + -5x = 0

Reorder the terms:
-5x + 5x3 = 0

Solving
-5x + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-1 + x2) = 0

Factor a difference between two squares.
5x((1 + x)(-1 + x)) = 0

Ignore the factor 5.

#### Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

#### Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

#### Subproblem 3

Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

x = {0, -1, 1}