E^3-E=0

Solution for E^3-E=0 equation:

Simplifying
E3 + -1E = 0

Reorder the terms:
-1E + E3 = 0

Solving
-1E + E3 = 0

Solving for variable 'E'.

Factor out the Greatest Common Factor (GCF), 'E'.
E(-1 + E2) = 0

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

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

Simplifying
E = 0

Solving
E = 0

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

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

Simplifying
1 + E = 0

Solving
1 + E = 0

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

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

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

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

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

Simplifying
-1 + E = 0

Solving
-1 + E = 0

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

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

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

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

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