z^2=5z

Solution for z^2=5z equation:

Simplifying
z2 = 5z

Solving
z2 = 5z

Solving for variable 'z'.

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

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

Factor out the Greatest Common Factor (GCF), 'z'.
z(-5 + 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 '(-5 + z)' equal to zero and attempt to solve:

Simplifying
-5 + z = 0

Solving
-5 + z = 0

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

Add '5' to each side of the equation.
-5 + 5 + z = 0 + 5

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

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

Simplifying
z = 5
Solution
z = {0, 5}