z^4-2z^2-8=0

Solution for z^4-2z^2-8=0 equation:

Simplifying
z4 + -2z2 + -8 = 0

Reorder the terms:
-8 + -2z2 + z4 = 0

Solving
-8 + -2z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z2)(4 + -1z2) = 0

Factor a difference between two squares.
(-2 + -1z2)((2 + z)(2 + -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 '(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}