6m^4-m^2-5=0

Solution for 6m^4-m^2-5=0 equation:

Simplifying
6m4 + -1m2 + -5 = 0

Reorder the terms:
-5 + -1m2 + 6m4 = 0

Solving
-5 + -1m2 + 6m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(-5 + -6m2)(1 + -1m2) = 0

Factor a difference between two squares.
(-5 + -6m2)((1 + m)(1 + -1m)) = 0

Subproblem 1
Set the factor '(-5 + -6m2)' equal to zero and attempt to solve:

Simplifying
-5 + -6m2 = 0

Solving
-5 + -6m2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6m2 = 0 + 5
-6m2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6m2 = 5

Divide each side by '-6'.
m2 = -0.8333333333

Simplifying
m2 = -0.8333333333

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

Simplifying
1 + m = 0

Solving
1 + m = 0

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

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

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

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

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

Simplifying
1 + -1m = 0

Solving
1 + -1m = 0

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

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

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

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

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

Simplifying
m = 1
Solution
m = {-1, 1}