n^4=625

Solution for n^4=625 equation:

Simplifying
n4 = 625

Solving
n4 = 625

Solving for variable 'n'.

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

Simplifying
n4 = 625

Reorder the terms:
-625 + n4 = 625 + -625

Combine like terms: 625 + -625 = 0
-625 + n4 = 0

Factor a difference between two squares.
(25 + n2)(-25 + n2) = 0

Factor a difference between two squares.
(25 + n2)((5 + n)(-5 + n)) = 0

Subproblem 1
Set the factor '(25 + n2)' equal to zero and attempt to solve:

Simplifying
25 + n2 = 0

Solving
25 + n2 = 0

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

Add '-25' to each side of the equation.
25 + -25 + n2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + n2 = 0 + -25
n2 = 0 + -25

Combine like terms: 0 + -25 = -25
n2 = -25

Simplifying
n2 = -25

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 '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 3
Set the factor '(-5 + n)' equal to zero and attempt to solve:

Simplifying
-5 + n = 0

Solving
-5 + n = 0

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

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

Combine like terms: -5 + 5 = 0
0 + n = 0 + 5
n = 0 + 5

Combine like terms: 0 + 5 = 5
n = 5

Simplifying
n = 5
Solution
n = {-5, 5}