0=x^4+x^2-12

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

Simplifying
0 = x4 + x2 + -12

Reorder the terms:
0 = -12 + x2 + x4

Solving
0 = -12 + x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + -1x2 + -1x4 = -12 + x2 + x4 + 12 + -1x2 + -1x4

Reorder the terms:
12 + -1x2 + -1x4 = -12 + 12 + x2 + -1x2 + x4 + -1x4

Combine like terms: -12 + 12 = 0
12 + -1x2 + -1x4 = 0 + x2 + -1x2 + x4 + -1x4
12 + -1x2 + -1x4 = x2 + -1x2 + x4 + -1x4

Combine like terms: x2 + -1x2 = 0
12 + -1x2 + -1x4 = 0 + x4 + -1x4
12 + -1x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
12 + -1x2 + -1x4 = 0

Factor a trinomial.
(3 + -1x2)(4 + x2) = 0

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

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

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

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

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(4 + x2)' equal to zero and attempt to solve:

Simplifying
4 + x2 = 0

Solving
4 + x2 = 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 + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 0 + -4
x2 = 0 + -4

Combine like terms: 0 + -4 = -4
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.
Solution
x = {-1.732050808, 1.732050808}