m^4=m^2+12

Solution for m^4=m^2+12 equation:

Simplifying
m4 = m2 + 12

Reorder the terms:
m4 = 12 + m2

Solving
m4 = 12 + m2

Solving for variable 'm'.

Reorder the terms:
-12 + -1m2 + m4 = 12 + m2 + -12 + -1m2

Reorder the terms:
-12 + -1m2 + m4 = 12 + -12 + m2 + -1m2

Combine like terms: 12 + -12 = 0
-12 + -1m2 + m4 = 0 + m2 + -1m2
-12 + -1m2 + m4 = m2 + -1m2

Combine like terms: m2 + -1m2 = 0
-12 + -1m2 + m4 = 0

Factor a trinomial.
(-3 + -1m2)(4 + -1m2) = 0

Factor a difference between two squares.
(-3 + -1m2)((2 + m)(2 + -1m)) = 0

Subproblem 1
Set the factor '(-3 + -1m2)' equal to zero and attempt to solve:

Simplifying
-3 + -1m2 = 0

Solving
-3 + -1m2 = 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 + -1m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m2 = 0 + 3
-1m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1m2 = 3

Divide each side by '-1'.
m2 = -3

Simplifying
m2 = -3

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 '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

Add '-2' to each side of the equation.
2 + -2 + m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + m = 0 + -2
m = 0 + -2

Combine like terms: 0 + -2 = -2
m = -2

Simplifying
m = -2
Subproblem 3
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-2, 2}