8w^3=8w

Solution for 8w^3=8w equation:

Simplifying
8w3 = 8w

Solving
8w3 = 8w

Solving for variable 'w'.

Reorder the terms:
-8w + 8w3 = 8w + -8w

Combine like terms: 8w + -8w = 0
-8w + 8w3 = 0

Factor out the Greatest Common Factor (GCF), '8w'.
8w(-1 + w2) = 0

Factor a difference between two squares.
8w((1 + w)(-1 + w)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

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

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

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

Simplifying
-1 + w = 0

Solving
-1 + w = 0

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

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

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

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

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