12x^4+4x^2-8=0

Solution for 12x^4+4x^2-8=0 equation:

Simplifying
12x4 + 4x2 + -8 = 0

Reorder the terms:
-8 + 4x2 + 12x4 = 0

Solving
-8 + 4x2 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + x2 + 3x4) = 0

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

Ignore the factor 4.
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 '(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

Take the square root of each side:
x = {-0.816496581, 0.816496581}
Solution
x = {-0.816496581, 0.816496581}