18x^4-6x^2-24=0

Solution for 18x^4-6x^2-24=0 equation:

Simplifying
18x4 + -6x2 + -24 = 0

Reorder the terms:
-24 + -6x2 + 18x4 = 0

Solving
-24 + -6x2 + 18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -1x2 + 3x4) = 0

Factor a trinomial.
6((-1 + -1x2)(4 + -3x2)) = 0

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

Simplifying
-1 + -1x2 = 0

Solving
-1 + -1x2 = 0

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

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

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

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

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

Simplifying
x2 = -1

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 '(4 + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x2 = 0

Solving
4 + -3x2 = 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 + -3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x2 = 0 + -4
-3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x2 = -4

Divide each side by '-3'.
x2 = 1.333333333

Simplifying
x2 = 1.333333333

Take the square root of each side:
x = {-1.154700538, 1.154700538}
Solution
x = {-1.154700538, 1.154700538}