6m^4-90m^2+300=0

Solution for 6m^4-90m^2+300=0 equation:

Simplifying
6m4 + -90m2 + 300 = 0

Reorder the terms:
300 + -90m2 + 6m4 = 0

Solving
300 + -90m2 + 6m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '6'.
6(50 + -15m2 + m4) = 0

Factor a trinomial.
6((5 + -1m2)(10 + -1m2)) = 0

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

Simplifying
5 + -1m2 = 0

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

Combine like terms: 5 + -5 = 0
0 + -1m2 = 0 + -5
-1m2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1m2 = -5

Divide each side by '-1'.
m2 = 5

Simplifying
m2 = 5

Take the square root of each side:
m = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(10 + -1m2)' equal to zero and attempt to solve:

Simplifying
10 + -1m2 = 0

Solving
10 + -1m2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1m2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1m2 = 0 + -10
-1m2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1m2 = -10

Divide each side by '-1'.
m2 = 10

Simplifying
m2 = 10

Take the square root of each side:
m = {-3.16227766, 3.16227766}
Solution
m = {-2.236067978, 2.236067978, -3.16227766, 3.16227766}