r^4-1=0

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Solution for r^4-1=0 equation: 


Simplifying
r4 + -1 = 0

Reorder the terms:
-1 + r4 = 0

Solving
-1 + r4 = 0

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + r4 = 0 + 1
r4 = 0 + 1

Combine like terms: 0 + 1 = 1
r4 = 1

Simplifying
r4 = 1

Reorder the terms:
-1 + r4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + r4 = 0

Factor a difference between two squares.
(1 + r2)(-1 + r2) = 0

Factor a difference between two squares.
(1 + r2)((1 + r)(-1 + r)) = 0


Subproblem 1
Set the factor '(1 + r2)' equal to zero and attempt to solve:

Simplifying
1 + r2 = 0

Solving
1 + r2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r2 = 0 + -1
r2 = 0 + -1

Combine like terms: 0 + -1 = -1
r2 = -1

Simplifying
r2 = -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 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

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

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

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

Simplifying
r = -1

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

Simplifying
-1 + r = 0

Solving
-1 + r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-1, 1}

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