z(z-5)=2z

Solution for z(z-5)=2z equation:

Simplifying
z(z + -5) = 2z

Reorder the terms:
z(-5 + z) = 2z
(-5 * z + z * z) = 2z
(-5z + z2) = 2z

Solving
-5z + z2 = 2z

Solving for variable 'z'.

Reorder the terms:
-5z + -2z + z2 = 2z + -2z

Combine like terms: -5z + -2z = -7z
-7z + z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
-7z + z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-7 + 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 '(-7 + z)' equal to zero and attempt to solve:

Simplifying
-7 + z = 0

Solving
-7 + z = 0

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

Add '7' to each side of the equation.
-7 + 7 + z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + z = 0 + 7
z = 0 + 7

Combine like terms: 0 + 7 = 7
z = 7

Simplifying
z = 7
Solution
z = {0, 7}