z^4+2z^2=0

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

Simplifying
z4 + 2z2 = 0

Reorder the terms:
2z2 + z4 = 0

Solving
2z2 + z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(2 + z2) = 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 '(2 + z2)' equal to zero and attempt to solve:

Simplifying
2 + z2 = 0

Solving
2 + z2 = 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 + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z2 = 0 + -2
z2 = 0 + -2

Combine like terms: 0 + -2 = -2
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.
Solution
z = {0}