r^4-4096=0

Solution for r^4-4096=0 equation:

Simplifying
r4 + -4096 = 0

Reorder the terms:
-4096 + r4 = 0

Solving
-4096 + r4 = 0

Solving for variable 'r'.

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

Add '4096' to each side of the equation.
-4096 + 4096 + r4 = 0 + 4096

Combine like terms: -4096 + 4096 = 0
0 + r4 = 0 + 4096
r4 = 0 + 4096

Combine like terms: 0 + 4096 = 4096
r4 = 4096

Simplifying
r4 = 4096

Reorder the terms:
-4096 + r4 = 4096 + -4096

Combine like terms: 4096 + -4096 = 0
-4096 + r4 = 0

Factor a difference between two squares.
(64 + r2)(-64 + r2) = 0

Factor a difference between two squares.
(64 + r2)((8 + r)(-8 + r)) = 0

Subproblem 1
Set the factor '(64 + r2)' equal to zero and attempt to solve:

Simplifying
64 + r2 = 0

Solving
64 + r2 = 0

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

Add '-64' to each side of the equation.
64 + -64 + r2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + r2 = 0 + -64
r2 = 0 + -64

Combine like terms: 0 + -64 = -64
r2 = -64

Simplifying
r2 = -64

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

Simplifying
8 + r = 0

Solving
8 + r = 0

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

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

Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8

Combine like terms: 0 + -8 = -8
r = -8

Simplifying
r = -8
Subproblem 3
Set the factor '(-8 + r)' equal to zero and attempt to solve:

Simplifying
-8 + r = 0

Solving
-8 + r = 0

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

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

Combine like terms: -8 + 8 = 0
0 + r = 0 + 8
r = 0 + 8

Combine like terms: 0 + 8 = 8
r = 8

Simplifying
r = 8
Solution
r = {-8, 8}