3x^4=16x^2+12

Solution for 3x^4=16x^2+12 equation:

Simplifying
3x4 = 16x2 + 12

Reorder the terms:
3x4 = 12 + 16x2

Solving
3x4 = 12 + 16x2

Solving for variable 'x'.

Reorder the terms:
-12 + -16x2 + 3x4 = 12 + 16x2 + -12 + -16x2

Reorder the terms:
-12 + -16x2 + 3x4 = 12 + -12 + 16x2 + -16x2

Combine like terms: 12 + -12 = 0
-12 + -16x2 + 3x4 = 0 + 16x2 + -16x2
-12 + -16x2 + 3x4 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-12 + -16x2 + 3x4 = 0

Factor a trinomial.
(-2 + -3x2)(6 + -1x2) = 0

Subproblem 1
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

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 '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-2.449489743, 2.449489743}