Z^4+Z^2-2=0

Solution for Z^4+Z^2-2=0 equation:

Simplifying
Z4 + Z2 + -2 = 0

Reorder the terms:
-2 + Z2 + Z4 = 0

Solving
-2 + Z2 + Z4 = 0

Solving for variable 'Z'.

Factor a trinomial.
(-2 + -1Z2)(1 + -1Z2) = 0

Factor a difference between two squares.
(-2 + -1Z2)((1 + Z)(1 + -1Z)) = 0

Subproblem 1
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

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 '(1 + Z)' equal to zero and attempt to solve:

Simplifying
1 + Z = 0

Solving
1 + Z = 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 + Z = 0 + -1

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

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

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

Simplifying
1 + -1Z = 0

Solving
1 + -1Z = 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 + -1Z = 0 + -1

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

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

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

Simplifying
Z = 1
Solution
Z = {-1, 1}