z^4-z^2-2=0

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

Simplifying
z4 + -1z2 + -2 = 0

Reorder the terms:
-2 + -1z2 + z4 = 0

Solving
-2 + -1z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z2)(2 + -1z2) = 0

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

Simplifying
-1 + -1z2 = 0

Solving
-1 + -1z2 = 0

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

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

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

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

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

Simplifying
z2 = -1

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

Simplifying
2 + -1z2 = 0

Solving
2 + -1z2 = 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 + -1z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z2 = 0 + -2
-1z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1z2 = -2

Divide each side by '-1'.
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Solution
z = {-1.414213562, 1.414213562}