2m^4-5m^2-3=0

Solution for 2m^4-5m^2-3=0 equation:

Simplifying
2m4 + -5m2 + -3 = 0

Reorder the terms:
-3 + -5m2 + 2m4 = 0

Solving
-3 + -5m2 + 2m4 = 0

Solving for variable 'm'.

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

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

Simplifying
-1 + -2m2 = 0

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

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

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

Divide each side by '-2'.
m2 = -0.5

Simplifying
m2 = -0.5

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 + -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

Take the square root of each side:
m = {-1.732050808, 1.732050808}
Solution
m = {-1.732050808, 1.732050808}