0=x^4-3x^2-108

Solution for 0=x^4-3x^2-108 equation:

Simplifying
0 = x4 + -3x2 + -108

Reorder the terms:
0 = -108 + -3x2 + x4

Solving
0 = -108 + -3x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 108 = 108
108 + 3x2 + -1x4 = -108 + -3x2 + x4 + 108 + 3x2 + -1x4

Reorder the terms:
108 + 3x2 + -1x4 = -108 + 108 + -3x2 + 3x2 + x4 + -1x4

Combine like terms: -108 + 108 = 0
108 + 3x2 + -1x4 = 0 + -3x2 + 3x2 + x4 + -1x4
108 + 3x2 + -1x4 = -3x2 + 3x2 + x4 + -1x4

Combine like terms: -3x2 + 3x2 = 0
108 + 3x2 + -1x4 = 0 + x4 + -1x4
108 + 3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
108 + 3x2 + -1x4 = 0

Factor a trinomial.
(12 + -1x2)(9 + x2) = 0

Subproblem 1
Set the factor '(12 + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -1x2 = 0

Solving
12 + -1x2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x2 = 0 + -12
-1x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1x2 = -12

Divide each side by '-1'.
x2 = 12

Simplifying
x2 = 12

Take the square root of each side:
x = {-3.464101615, 3.464101615}
Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-3.464101615, 3.464101615}