5q^4-5n^4=0

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

Simplifying
5q4 + -5n4 = 0

Reorder the terms:
-5n4 + 5q4 = 0

Solving
-5n4 + 5q4 = 0

Solving for variable 'n'.

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

Add '-5q4' to each side of the equation.
-5n4 + 5q4 + -5q4 = 0 + -5q4

Combine like terms: 5q4 + -5q4 = 0
-5n4 + 0 = 0 + -5q4
-5n4 = 0 + -5q4
Remove the zero:
-5n4 = -5q4

Divide each side by '-5'.
n4 = q4

Simplifying
n4 = q4

Combine like terms: q4 + -1q4 = 0
n4 + -1q4 = 0

Factor a difference between two squares.
(n2 + q2)(n2 + -1q2) = 0

Factor a difference between two squares.
(n2 + q2)((n + q)(n + -1q)) = 0

Subproblem 1
Set the factor '(n2 + q2)' equal to zero and attempt to solve:

Simplifying
n2 + q2 = 0

Solving
n2 + q2 = 0

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

Add '-1q2' to each side of the equation.
n2 + q2 + -1q2 = 0 + -1q2

Combine like terms: q2 + -1q2 = 0
n2 + 0 = 0 + -1q2
n2 = 0 + -1q2
Remove the zero:
n2 = -1q2

Simplifying
n2 = -1q2

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

Simplifying
n + q = 0

Solving
n + q = 0

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

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

Combine like terms: q + -1q = 0
n + 0 = 0 + -1q
n = 0 + -1q
Remove the zero:
n = -1q

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

Simplifying
n + -1q = 0

Solving
n + -1q = 0

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

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

Combine like terms: -1q + q = 0
n + 0 = 0 + q
n = 0 + q
Remove the zero:
n = q

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