q^2-q^4+72=0

Solution for q^2-q^4+72=0 equation:

Simplifying
q2 + -1q4 + 72 = 0

Reorder the terms:
72 + q2 + -1q4 = 0

Solving
72 + q2 + -1q4 = 0

Solving for variable 'q'.

Factor a trinomial.
(9 + -1q2)(8 + q2) = 0

Factor a difference between two squares.
((3 + q)(3 + -1q))(8 + q2) = 0

Subproblem 1
Set the factor '(8 + q2)' equal to zero and attempt to solve:

Simplifying
8 + q2 = 0

Solving
8 + q2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + q2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + q2 = 0 + -8
q2 = 0 + -8

Combine like terms: 0 + -8 = -8
q2 = -8

Simplifying
q2 = -8

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 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 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 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

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