4z^4=-4z^2

Solution for 4z^4=-4z^2 equation:

Simplifying
4z4 = -4z2

Solving
4z4 = -4z2

Solving for variable 'z'.

Reorder the terms:
4z2 + 4z4 = -4z2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
4z2 + 4z4 = 0

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(1 + z2) = 0

Ignore the factor 4.
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 '(1 + z2)' equal to zero and attempt to solve:

Simplifying
1 + z2 = 0

Solving
1 + z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z2 = 0 + -1
z2 = 0 + -1

Combine like terms: 0 + -1 = -1
z2 = -1

Simplifying
z2 = -1

The solution to this equation could not be determined.

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