5n^4-80=0

Solution for 5n^4-80=0 equation:

Simplifying
5n4 + -80 = 0

Reorder the terms:
-80 + 5n4 = 0

Solving
-80 + 5n4 = 0

Solving for variable 'n'.

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

Add '80' to each side of the equation.
-80 + 80 + 5n4 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 5n4 = 0 + 80
5n4 = 0 + 80

Combine like terms: 0 + 80 = 80
5n4 = 80

Divide each side by '5'.
n4 = 16

Simplifying
n4 = 16

Reorder the terms:
-16 + n4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + n4 = 0

Factor a difference between two squares.
(4 + n2)(-4 + n2) = 0

Factor a difference between two squares.
(4 + n2)((2 + n)(-2 + n)) = 0

Subproblem 1
Set the factor '(4 + n2)' equal to zero and attempt to solve:

Simplifying
4 + n2 = 0

Solving
4 + n2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n2 = 0 + -4
n2 = 0 + -4

Combine like terms: 0 + -4 = -4
n2 = -4

Simplifying
n2 = -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 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

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

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

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

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

Simplifying
-2 + n = 0

Solving
-2 + n = 0

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

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

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

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

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