r^4-81=0

Solution for r^4-81=0 equation:

Simplifying
r4 + -81 = 0

Reorder the terms:
-81 + r4 = 0

Solving
-81 + r4 = 0

Solving for variable 'r'.

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

Add '81' to each side of the equation.
-81 + 81 + r4 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + r4 = 0 + 81
r4 = 0 + 81

Combine like terms: 0 + 81 = 81
r4 = 81

Simplifying
r4 = 81

Reorder the terms:
-81 + r4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + r4 = 0

Factor a difference between two squares.
(9 + r2)(-9 + r2) = 0

Factor a difference between two squares.
(9 + r2)((3 + r)(-3 + r)) = 0

Subproblem 1
Set the factor '(9 + r2)' equal to zero and attempt to solve:

Simplifying
9 + r2 = 0

Solving
9 + r2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + r2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + r2 = 0 + -9
r2 = 0 + -9

Combine like terms: 0 + -9 = -9
r2 = -9

Simplifying
r2 = -9

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

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

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

Simplifying
-3 + r = 0

Solving
-3 + r = 0

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

Add '3' to each side of the equation.
-3 + 3 + r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + r = 0 + 3
r = 0 + 3

Combine like terms: 0 + 3 = 3
r = 3

Simplifying
r = 3
Solution
r = {-3, 3}