2m^4=3m^2+5

Solution for 2m^4=3m^2+5 equation:

Simplifying
2m4 = 3m2 + 5

Reorder the terms:
2m4 = 5 + 3m2

Solving
2m4 = 5 + 3m2

Solving for variable 'm'.

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

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

Combine like terms: 5 + -5 = 0
-5 + -3m2 + 2m4 = 0 + 3m2 + -3m2
-5 + -3m2 + 2m4 = 3m2 + -3m2

Combine like terms: 3m2 + -3m2 = 0
-5 + -3m2 + 2m4 = 0

Factor a trinomial.
(-1 + -1m2)(5 + -2m2) = 0

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

Simplifying
-1 + -1m2 = 0

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

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

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

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

Simplifying
m2 = -1

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 '(5 + -2m2)' equal to zero and attempt to solve:

Simplifying
5 + -2m2 = 0

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

Combine like terms: 5 + -5 = 0
0 + -2m2 = 0 + -5
-2m2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2m2 = -5

Divide each side by '-2'.
m2 = 2.5

Simplifying
m2 = 2.5

Take the square root of each side:
m = {-1.58113883, 1.58113883}
Solution
m = {-1.58113883, 1.58113883}