3z-z(6-z)=0

Solution for 3z-z(6-z)=0 equation:

Simplifying
3z + -1z(6 + -1z) = 0
3z + (6 * -1z + -1z * -1z) = 0
3z + (-6z + 1z2) = 0

Combine like terms: 3z + -6z = -3z
-3z + 1z2 = 0

Solving
-3z + 1z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-3 + 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 '(-3 + z)' equal to zero and attempt to solve:

Simplifying
-3 + z = 0

Solving
-3 + z = 0

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

Add '3' to each side of the equation.
-3 + 3 + z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + z = 0 + 3
z = 0 + 3

Combine like terms: 0 + 3 = 3
z = 3

Simplifying
z = 3
Solution
z = {0, 3}