w^4-1=0

Solution for w^4-1=0 equation:

Simplifying
w4 + -1 = 0

Reorder the terms:
-1 + w4 = 0

Solving
-1 + w4 = 0

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + w4 = 0 + 1
w4 = 0 + 1

Combine like terms: 0 + 1 = 1
w4 = 1

Simplifying
w4 = 1

Reorder the terms:
-1 + w4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + w4 = 0

Factor a difference between two squares.
(1 + w2)(-1 + w2) = 0

Factor a difference between two squares.
(1 + w2)((1 + w)(-1 + w)) = 0

Subproblem 1
Set the factor '(1 + w2)' equal to zero and attempt to solve:

Simplifying
1 + w2 = 0

Solving
1 + w2 = 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 + w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + w2 = 0 + -1
w2 = 0 + -1

Combine like terms: 0 + -1 = -1
w2 = -1

Simplifying
w2 = -1

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}