3x^4-6x^2=45

Solution for 3x^4-6x^2=45 equation:

Simplifying
3x4 + -6x2 = 45

Reorder the terms:
-6x2 + 3x4 = 45

Solving
-6x2 + 3x4 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -6x2 + 3x4 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -6x2 + 3x4 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x2 + x4) = 0

Factor a trinomial.
3((-3 + -1x2)(5 + -1x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -3

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 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

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