5q^4-5=0

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

Simplifying
5q4 + -5 = 0

Reorder the terms:
-5 + 5q4 = 0

Solving
-5 + 5q4 = 0

Solving for variable 'q'.

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

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

Combine like terms: -5 + 5 = 0
0 + 5q4 = 0 + 5
5q4 = 0 + 5

Combine like terms: 0 + 5 = 5
5q4 = 5

Divide each side by '5'.
q4 = 1

Simplifying
q4 = 1

Reorder the terms:
-1 + q4 = 1 + -1

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

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

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

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

Simplifying
1 + q2 = 0

Solving
1 + q2 = 0

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

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

Combine like terms: 1 + -1 = 0
0 + q2 = 0 + -1
q2 = 0 + -1

Combine like terms: 0 + -1 = -1
q2 = -1

Simplifying
q2 = -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 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 0

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

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

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

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

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

Simplifying
-1 + q = 0

Solving
-1 + q = 0

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

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

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

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

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