z^4+z^2-12=0

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

Simplifying
z4 + z2 + -12 = 0

Reorder the terms:
-12 + z2 + z4 = 0

Solving
-12 + z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z2)(3 + -1z2) = 0

Subproblem 1
Set the factor '(-4 + -1z2)' equal to zero and attempt to solve:

Simplifying
-4 + -1z2 = 0

Solving
-4 + -1z2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z2 = 0 + 4
-1z2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1z2 = 4

Divide each side by '-1'.
z2 = -4

Simplifying
z2 = -4

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 '(3 + -1z2)' equal to zero and attempt to solve:

Simplifying
3 + -1z2 = 0

Solving
3 + -1z2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z2 = 0 + -3
-1z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1z2 = -3

Divide each side by '-1'.
z2 = 3

Simplifying
z2 = 3

Take the square root of each side:
z = {-1.732050808, 1.732050808}
Solution
z = {-1.732050808, 1.732050808}