12x^4-28x^2-24=0

Solution for 12x^4-28x^2-24=0 equation:

Simplifying
12x4 + -28x2 + -24 = 0

Reorder the terms:
-24 + -28x2 + 12x4 = 0

Solving
-24 + -28x2 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -7x2 + 3x4) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -3x2)' equal to zero and attempt to solve:

Simplifying
-2 + -3x2 = 0

Solving
-2 + -3x2 = 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 + -3x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x2 = 0 + 2
-3x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3x2 = 2

Divide each side by '-3'.
x2 = -0.6666666667

Simplifying
x2 = -0.6666666667

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 '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

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

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

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}