8r^4-128=0

Solution for 8r^4-128=0 equation:

Simplifying
8r4 + -128 = 0

Reorder the terms:
-128 + 8r4 = 0

Solving
-128 + 8r4 = 0

Solving for variable 'r'.

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

Add '128' to each side of the equation.
-128 + 128 + 8r4 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 8r4 = 0 + 128
8r4 = 0 + 128

Combine like terms: 0 + 128 = 128
8r4 = 128

Divide each side by '8'.
r4 = 16

Simplifying
r4 = 16

Reorder the terms:
-16 + r4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + r4 = 0

Factor a difference between two squares.
(4 + r2)(-4 + r2) = 0

Factor a difference between two squares.
(4 + r2)((2 + r)(-2 + r)) = 0

Subproblem 1
Set the factor '(4 + r2)' equal to zero and attempt to solve:

Simplifying
4 + r2 = 0

Solving
4 + r2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r2 = 0 + -4
r2 = 0 + -4

Combine like terms: 0 + -4 = -4
r2 = -4

Simplifying
r2 = -4

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 '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

Simplifying
r = -2
Subproblem 3
Set the factor '(-2 + r)' equal to zero and attempt to solve:

Simplifying
-2 + r = 0

Solving
-2 + r = 0

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

Add '2' to each side of the equation.
-2 + 2 + r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + r = 0 + 2
r = 0 + 2

Combine like terms: 0 + 2 = 2
r = 2

Simplifying
r = 2
Solution
r = {-2, 2}