(X^4-1)=0

Solution for (X^4-1)=0 equation:

Simplifying
(X4 + -1) = 0

Reorder the terms:
(-1 + X4) = 0

Remove parenthesis around (-1 + X4)
-1 + X4 = 0

Solving
-1 + X4 = 0

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + X4 = 0 + 1
X4 = 0 + 1

Combine like terms: 0 + 1 = 1
X4 = 1

Simplifying
X4 = 1

Reorder the terms:
-1 + X4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + X4 = 0

Factor a difference between two squares.
(1 + X2)(-1 + X2) = 0

Factor a difference between two squares.
(1 + X2)((1 + X)(-1 + X)) = 0

Subproblem 1
Set the factor '(1 + X2)' equal to zero and attempt to solve:

Simplifying
1 + X2 = 0

Solving
1 + X2 = 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 + X2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + X2 = 0 + -1
X2 = 0 + -1

Combine like terms: 0 + -1 = -1
X2 = -1

Simplifying
X2 = -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 + 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
Solution
X = {-1, 1}