3x^4-6x^2-24=0

Solution for 3x^4-6x^2-24=0 equation:

Simplifying
3x4 + -6x2 + -24 = 0

Reorder the terms:
-24 + -6x2 + 3x4 = 0

Solving
-24 + -6x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2x2 + x4) = 0

Factor a trinomial.
3((-2 + -1x2)(4 + -1x2)) = 0

Factor a difference between two squares.
3((-2 + -1x2)((2 + x)(2 + -1x))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve:

Simplifying
-2 + -1x2 = 0

Solving
-2 + -1x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x2 = 0 + 2
-1x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1x2 = 2

Divide each side by '-1'.
x2 = -2

Simplifying
x2 = -2

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}