Z^4+12Z^2-64=0

Solution for Z^4+12Z^2-64=0 equation:

Simplifying
Z4 + 12Z2 + -64 = 0

Reorder the terms:
-64 + 12Z2 + Z4 = 0

Solving
-64 + 12Z2 + Z4 = 0

Solving for variable 'Z'.

Factor a trinomial.
(-16 + -1Z2)(4 + -1Z2) = 0

Factor a difference between two squares.
(-16 + -1Z2)((2 + Z)(2 + -1Z)) = 0

Subproblem 1
Set the factor '(-16 + -1Z2)' equal to zero and attempt to solve:

Simplifying
-16 + -1Z2 = 0

Solving
-16 + -1Z2 = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1Z2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1Z2 = 0 + 16
-1Z2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1Z2 = 16

Divide each side by '-1'.
Z2 = -16

Simplifying
Z2 = -16

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}