z^6+4z^2=0

Solution for z^6+4z^2=0 equation:

Simplifying
z6 + 4z2 = 0

Reorder the terms:
4z2 + z6 = 0

Solving
4z2 + z6 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(4 + z4) = 0

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(4 + z4)' equal to zero and attempt to solve:

Simplifying
4 + z4 = 0

Solving
4 + z4 = 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 + z4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z4 = 0 + -4
z4 = 0 + -4

Combine like terms: 0 + -4 = -4
z4 = -4

Simplifying
z4 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}