3x^4-2x^2+12x^2-8=0

Solution for 3x^4-2x^2+12x^2-8=0 equation:

Simplifying
3x4 + -2x2 + 12x2 + -8 = 0

Reorder the terms:
-8 + -2x2 + 12x2 + 3x4 = 0

Combine like terms: -2x2 + 12x2 = 10x2
-8 + 10x2 + 3x4 = 0

Solving
-8 + 10x2 + 3x4 = 0

Solving for variable 'x'.

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