5q^4-405=0

Solution for 5q^4-405=0 equation:

Simplifying
5q4 + -405 = 0

Reorder the terms:
-405 + 5q4 = 0

Solving
-405 + 5q4 = 0

Solving for variable 'q'.

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

Add '405' to each side of the equation.
-405 + 405 + 5q4 = 0 + 405

Combine like terms: -405 + 405 = 0
0 + 5q4 = 0 + 405
5q4 = 0 + 405

Combine like terms: 0 + 405 = 405
5q4 = 405

Divide each side by '5'.
q4 = 81

Simplifying
q4 = 81

Reorder the terms:
-81 + q4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + q4 = 0

Factor a difference between two squares.
(9 + q2)(-9 + q2) = 0

Factor a difference between two squares.
(9 + q2)((3 + q)(-3 + q)) = 0

Subproblem 1
Set the factor '(9 + q2)' equal to zero and attempt to solve:

Simplifying
9 + q2 = 0

Solving
9 + q2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + q2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + q2 = 0 + -9
q2 = 0 + -9

Combine like terms: 0 + -9 = -9
q2 = -9

Simplifying
q2 = -9

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

Simplifying
3 + q = 0

Solving
3 + q = 0

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

Add '-3' to each side of the equation.
3 + -3 + q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + q = 0 + -3
q = 0 + -3

Combine like terms: 0 + -3 = -3
q = -3

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

Simplifying
-3 + q = 0

Solving
-3 + q = 0

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

Add '3' to each side of the equation.
-3 + 3 + q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + q = 0 + 3
q = 0 + 3

Combine like terms: 0 + 3 = 3
q = 3

Simplifying
q = 3
Solution
q = {-3, 3}