6m^4+4m^2-16=0

Solution for 6m^4+4m^2-16=0 equation:

Simplifying
6m4 + 4m2 + -16 = 0

Reorder the terms:
-16 + 4m2 + 6m4 = 0

Solving
-16 + 4m2 + 6m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 2m2 + 3m4) = 0

Factor a trinomial.
2((-2 + -1m2)(4 + -3m2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -1m2)' equal to zero and attempt to solve:

Simplifying
-2 + -1m2 = 0

Solving
-2 + -1m2 = 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 + -1m2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1m2 = 0 + 2
-1m2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1m2 = 2

Divide each side by '-1'.
m2 = -2

Simplifying
m2 = -2

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 '(4 + -3m2)' equal to zero and attempt to solve:

Simplifying
4 + -3m2 = 0

Solving
4 + -3m2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3m2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3m2 = 0 + -4
-3m2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3m2 = -4

Divide each side by '-3'.
m2 = 1.333333333

Simplifying
m2 = 1.333333333

Take the square root of each side:
m = {-1.154700538, 1.154700538}
Solution
m = {-1.154700538, 1.154700538}