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

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

Simplifying
4x2 + -6x4 + 2 = 0

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

Solving
2 + 4x2 + -6x4 = 0

Solving for variable 'x'.

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

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-1, 1}