0=x^4-133-12x^2

Solution for 0=x^4-133-12x^2 equation:

Simplifying
0 = x4 + -133 + -12x2

Reorder the terms:
0 = -133 + -12x2 + x4

Solving
0 = -133 + -12x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 133 = 133
133 + 12x2 + -1x4 = -133 + -12x2 + x4 + 133 + 12x2 + -1x4

Reorder the terms:
133 + 12x2 + -1x4 = -133 + 133 + -12x2 + 12x2 + x4 + -1x4

Combine like terms: -133 + 133 = 0
133 + 12x2 + -1x4 = 0 + -12x2 + 12x2 + x4 + -1x4
133 + 12x2 + -1x4 = -12x2 + 12x2 + x4 + -1x4

Combine like terms: -12x2 + 12x2 = 0
133 + 12x2 + -1x4 = 0 + x4 + -1x4
133 + 12x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
133 + 12x2 + -1x4 = 0

Factor a trinomial.
(19 + -1x2)(7 + x2) = 0

Subproblem 1
Set the factor '(19 + -1x2)' equal to zero and attempt to solve:

Simplifying
19 + -1x2 = 0

Solving
19 + -1x2 = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x2 = 0 + -19
-1x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-1x2 = -19

Divide each side by '-1'.
x2 = 19

Simplifying
x2 = 19

Take the square root of each side:
x = {-4.358898944, 4.358898944}
Subproblem 2
Set the factor '(7 + x2)' equal to zero and attempt to solve:

Simplifying
7 + x2 = 0

Solving
7 + x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x2 = 0 + -7
x2 = 0 + -7

Combine like terms: 0 + -7 = -7
x2 = -7

Simplifying
x2 = -7

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-4.358898944, 4.358898944}