v^4-81=0

Solution for v^4-81=0 equation:

Simplifying
v4 + -81 = 0

Reorder the terms:
-81 + v4 = 0

Solving
-81 + v4 = 0

Solving for variable 'v'.

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

Add '81' to each side of the equation.
-81 + 81 + v4 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + v4 = 0 + 81
v4 = 0 + 81

Combine like terms: 0 + 81 = 81
v4 = 81

Simplifying
v4 = 81

Reorder the terms:
-81 + v4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + v4 = 0

Factor a difference between two squares.
(9 + v2)(-9 + v2) = 0

Factor a difference between two squares.
(9 + v2)((3 + v)(-3 + v)) = 0

Subproblem 1
Set the factor '(9 + v2)' equal to zero and attempt to solve:

Simplifying
9 + v2 = 0

Solving
9 + v2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + v2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + v2 = 0 + -9
v2 = 0 + -9

Combine like terms: 0 + -9 = -9
v2 = -9

Simplifying
v2 = -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 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 0

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

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

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

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

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

Simplifying
-3 + v = 0

Solving
-3 + v = 0

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

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

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

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

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