z(z-1)=0

Solution for z(z-1)=0 equation:

Simplifying
z(z + -1) = 0

Reorder the terms:
z(-1 + z) = 0
(-1 * z + z * z) = 0
(-1z + z2) = 0

Solving
-1z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
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
Solution
z = {0, 1}