5z^2=5z

Solution for 5z^2=5z equation:

Simplifying
5z2 = 5z

Solving
5z2 = 5z

Solving for variable 'z'.

Reorder the terms:
-5z + 5z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-5z + 5z2 = 0

Factor out the Greatest Common Factor (GCF), '5z'.
5z(-1 + z) = 0

Ignore the factor 5.
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}