z^4=z^2

Solution for z^4=z^2 equation:

Simplifying
z4 = z2

Solving
z4 = z2

Solving for variable 'z'.

Reorder the terms:
-1z2 + z4 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-1z2 + z4 = 0

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

Factor a difference between two squares.
z2((1 + z)(-1 + z)) = 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 '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

Simplifying
z = -1
Subproblem 3
Set the factor '(-1 + z)' equal to zero and attempt to solve:

Simplifying
-1 + z = 0

Solving
-1 + z = 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 + z = 0 + 1

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

Combine like terms: 0 + 1 = 1
z = 1

Simplifying
z = 1
Solution
z = {0, -1, 1}