z^4-z^2-12=0

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

Simplifying
z4 + -1z2 + -12 = 0

Reorder the terms:
-12 + -1z2 + z4 = 0

Solving
-12 + -1z2 + z4 = 0

Solving for variable 'z'.

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

Factor a difference between two squares.
(-3 + -1z2)((2 + z)(2 + -1z)) = 0

Subproblem 1
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

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 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

Add '-2' to each side of the equation.
2 + -2 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

Simplifying
z = -2
Subproblem 3
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-2, 2}