12x^4=2x^2+4

Solution for 12x^4=2x^2+4 equation:

Simplifying
12x4 = 2x2 + 4

Reorder the terms:
12x4 = 4 + 2x2

Solving
12x4 = 4 + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -2x2 + 12x4 = 4 + 2x2 + -4 + -2x2

Reorder the terms:
-4 + -2x2 + 12x4 = 4 + -4 + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + -2x2 + 12x4 = 0 + 2x2 + -2x2
-4 + -2x2 + 12x4 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + -2x2 + 12x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1x2 + 6x4) = 0

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

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

Simplifying
-1 + -2x2 = 0

Solving
-1 + -2x2 = 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 + -2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x2 = 0 + 1
-2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2x2 = 1

Divide each side by '-2'.
x2 = -0.5

Simplifying
x2 = -0.5

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}