0=6x^4+4x^2-2

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

Simplifying
0 = 6x4 + 4x2 + -2

Reorder the terms:
0 = -2 + 4x2 + 6x4

Solving
0 = -2 + 4x2 + 6x4

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -4x2 + -6x4 = -2 + 4x2 + 6x4 + 2 + -4x2 + -6x4

Reorder the terms:
2 + -4x2 + -6x4 = -2 + 2 + 4x2 + -4x2 + 6x4 + -6x4

Combine like terms: -2 + 2 = 0
2 + -4x2 + -6x4 = 0 + 4x2 + -4x2 + 6x4 + -6x4
2 + -4x2 + -6x4 = 4x2 + -4x2 + 6x4 + -6x4

Combine like terms: 4x2 + -4x2 = 0
2 + -4x2 + -6x4 = 0 + 6x4 + -6x4
2 + -4x2 + -6x4 = 6x4 + -6x4

Combine like terms: 6x4 + -6x4 = 0
2 + -4x2 + -6x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2x2 + -3x4) = 0

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

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

Simplifying
1 + -3x2 = 0

Solving
1 + -3x2 = 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 + -3x2 = 0 + -1

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

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

Divide each side by '-3'.
x2 = 0.3333333333

Simplifying
x2 = 0.3333333333

Take the square root of each side:
x = {-0.577350269, 0.577350269}
Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

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

Combine like terms: 0 + -1 = -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.
Solution
x = {-0.577350269, 0.577350269}