(z-3)(z-6)=

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

Simplifying
(z + -3)(z + -6) = 0

Reorder the terms:
(-3 + z)(z + -6) = 0

Reorder the terms:
(-3 + z)(-6 + z) = 0

Multiply (-3 + z) * (-6 + z)
(-3(-6 + z) + z(-6 + z)) = 0
((-6 * -3 + z * -3) + z(-6 + z)) = 0
((18 + -3z) + z(-6 + z)) = 0
(18 + -3z + (-6 * z + z * z)) = 0
(18 + -3z + (-6z + z2)) = 0

Combine like terms: -3z + -6z = -9z
(18 + -9z + z2) = 0

Solving
18 + -9z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(6 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

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

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

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {3, 6}