z^4+0.2*z^2=0

Solution for z^4+0.2*z^2=0 equation:

Simplifying
z4 + 0.2z2 = 0

Reorder the terms:
0.2z2 + z4 = 0

Solving
0.2z2 + z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(0.2 + 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 '(0.2 + z2)' equal to zero and attempt to solve:

Simplifying
0.2 + z2 = 0

Solving
0.2 + z2 = 0

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + z2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + z2 = 0 + -0.2
z2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
z2 = -0.2

Simplifying
z2 = -0.2

The solution to this equation could not be determined.

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