m^4-m^2-72=0

Solution for m^4-m^2-72=0 equation:

Simplifying
m4 + -1m2 + -72 = 0

Reorder the terms:
-72 + -1m2 + m4 = 0

Solving
-72 + -1m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(-8 + -1m2)(9 + -1m2) = 0

Factor a difference between two squares.
(-8 + -1m2)((3 + m)(3 + -1m)) = 0

Subproblem 1
Set the factor '(-8 + -1m2)' equal to zero and attempt to solve:

Simplifying
-8 + -1m2 = 0

Solving
-8 + -1m2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1m2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1m2 = 0 + 8
-1m2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1m2 = 8

Divide each side by '-1'.
m2 = -8

Simplifying
m2 = -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 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

Solving
3 + m = 0

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

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

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

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

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

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

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

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

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

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