15x^4-108x^2+108=0

Solution for 15x^4-108x^2+108=0 equation:

Simplifying
15x4 + -108x2 + 108 = 0

Reorder the terms:
108 + -108x2 + 15x4 = 0

Solving
108 + -108x2 + 15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + -36x2 + 5x4) = 0

Factor a trinomial.
3((6 + -5x2)(6 + -1x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -5x2)' equal to zero and attempt to solve:

Simplifying
6 + -5x2 = 0

Solving
6 + -5x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x2 = 0 + -6
-5x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-5x2 = -6

Divide each side by '-5'.
x2 = 1.2

Simplifying
x2 = 1.2

Take the square root of each side:
x = {-1.095445115, 1.095445115}
Subproblem 2
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-1.095445115, 1.095445115, -2.449489743, 2.449489743}