(z^4-16)(z^4+16)=0

Solution for (z^4-16)(z^4+16)=0 equation:

Simplifying
(z4 + -16)(z4 + 16) = 0

Reorder the terms:
(-16 + z4)(z4 + 16) = 0

Reorder the terms:
(-16 + z4)(16 + z4) = 0

Multiply (-16 + z4) * (16 + z4)
(-16(16 + z4) + z4(16 + z4)) = 0
((16 * -16 + z4 * -16) + z4(16 + z4)) = 0
((-256 + -16z4) + z4(16 + z4)) = 0
(-256 + -16z4 + (16 * z4 + z4 * z4)) = 0
(-256 + -16z4 + (16z4 + z8)) = 0

Combine like terms: -16z4 + 16z4 = 0
(-256 + 0 + z8) = 0
(-256 + z8) = 0

Solving
-256 + z8 = 0

Solving for variable 'z'.

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

Add '256' to each side of the equation.
-256 + 256 + z8 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + z8 = 0 + 256
z8 = 0 + 256

Combine like terms: 0 + 256 = 256
z8 = 256

Simplifying
z8 = 256

Reorder the terms:
-256 + z8 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + z8 = 0

Factor a difference between two squares.
(16 + z4)(-16 + z4) = 0

Factor a difference between two squares.
(16 + z4)((4 + z2)(-4 + z2)) = 0

Factor a difference between two squares.
(16 + z4)((4 + z2)((2 + z)(-2 + z))) = 0

Subproblem 1
Set the factor '(16 + z4)' equal to zero and attempt to solve:

Simplifying
16 + z4 = 0

Solving
16 + z4 = 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 + z4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + z4 = 0 + -16
z4 = 0 + -16

Combine like terms: 0 + -16 = -16
z4 = -16

Simplifying
z4 = -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 '(4 + z2)' equal to zero and attempt to solve:

Simplifying
4 + z2 = 0

Solving
4 + z2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z2 = 0 + -4
z2 = 0 + -4

Combine like terms: 0 + -4 = -4
z2 = -4

Simplifying
z2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
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 4
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
Solution
z = {-2, 2}