w^5-w^3=0

Solution for w^5-w^3=0 equation:

Simplifying
w5 + -1w3 = 0

Reorder the terms:
-1w3 + w5 = 0

Solving
-1w3 + w5 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w3'.
w3(-1 + w2) = 0

Factor a difference between two squares.
w3((1 + w)(-1 + w)) = 0

Subproblem 1
Set the factor 'w3' equal to zero and attempt to solve:

Simplifying
w3 = 0

Solving
w3 = 0

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

Simplifying
w3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-1, 1}