7n^4-7=0

Solution for 7n^4-7=0 equation:

Simplifying
7n4 + -7 = 0

Reorder the terms:
-7 + 7n4 = 0

Solving
-7 + 7n4 = 0

Solving for variable 'n'.

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

Add '7' to each side of the equation.
-7 + 7 + 7n4 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 7n4 = 0 + 7
7n4 = 0 + 7

Combine like terms: 0 + 7 = 7
7n4 = 7

Divide each side by '7'.
n4 = 1

Simplifying
n4 = 1

Reorder the terms:
-1 + n4 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + n4 = 0

Factor a difference between two squares.
(1 + n2)(-1 + n2) = 0

Factor a difference between two squares.
(1 + n2)((1 + n)(-1 + n)) = 0

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

Simplifying
1 + n2 = 0

Solving
1 + n2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n2 = 0 + -1
n2 = 0 + -1

Combine like terms: 0 + -1 = -1
n2 = -1

Simplifying
n2 = -1

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Subproblem 3
Set the factor '(-1 + n)' equal to zero and attempt to solve:

Simplifying
-1 + n = 0

Solving
-1 + n = 0

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

Add '1' to each side of the equation.
-1 + 1 + n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0 + 1
n = 0 + 1

Combine like terms: 0 + 1 = 1
n = 1

Simplifying
n = 1
Solution
n = {-1, 1}