3(z-9)-z(z-9)=0

Solution for 3(z-9)-z(z-9)=0 equation:

Simplifying
3(z + -9) + -1z(z + -9) = 0

Reorder the terms:
3(-9 + z) + -1z(z + -9) = 0
(-9 * 3 + z * 3) + -1z(z + -9) = 0
(-27 + 3z) + -1z(z + -9) = 0

Reorder the terms:
-27 + 3z + -1z(-9 + z) = 0
-27 + 3z + (-9 * -1z + z * -1z) = 0
-27 + 3z + (9z + -1z2) = 0

Combine like terms: 3z + 9z = 12z
-27 + 12z + -1z2 = 0

Solving
-27 + 12z + -1z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-9 + z)' equal to zero and attempt to solve:

Simplifying
-9 + z = 0

Solving
-9 + z = 0

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

Add '9' to each side of the equation.
-9 + 9 + z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + z = 0 + 9
z = 0 + 9

Combine like terms: 0 + 9 = 9
z = 9

Simplifying
z = 9
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {9, 3}