(x^2-2)(x^2-2)+3x^2-6-18=0

Solution for (x^2-2)(x^2-2)+3x^2-6-18=0 equation:

Simplifying
(x2 + -2)(x2 + -2) + 3x2 + -6 + -18 = 0

Reorder the terms:
(-2 + x2)(x2 + -2) + 3x2 + -6 + -18 = 0

Reorder the terms:
(-2 + x2)(-2 + x2) + 3x2 + -6 + -18 = 0

Multiply (-2 + x2) * (-2 + x2)
(-2(-2 + x2) + x2(-2 + x2)) + 3x2 + -6 + -18 = 0
((-2 * -2 + x2 * -2) + x2(-2 + x2)) + 3x2 + -6 + -18 = 0
((4 + -2x2) + x2(-2 + x2)) + 3x2 + -6 + -18 = 0
(4 + -2x2 + (-2 * x2 + x2 * x2)) + 3x2 + -6 + -18 = 0
(4 + -2x2 + (-2x2 + x4)) + 3x2 + -6 + -18 = 0

Combine like terms: -2x2 + -2x2 = -4x2
(4 + -4x2 + x4) + 3x2 + -6 + -18 = 0

Reorder the terms:
4 + -6 + -18 + -4x2 + 3x2 + x4 = 0

Combine like terms: 4 + -6 = -2
-2 + -18 + -4x2 + 3x2 + x4 = 0

Combine like terms: -2 + -18 = -20
-20 + -4x2 + 3x2 + x4 = 0

Combine like terms: -4x2 + 3x2 = -1x2
-20 + -1x2 + x4 = 0

Solving
-20 + -1x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x2)(5 + -1x2) = 0

Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

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}