(z-6)(z-5)=0

Solution for (z-6)(z-5)=0 equation:

Simplifying
(z + -6)(z + -5) = 0

Reorder the terms:
(-6 + z)(z + -5) = 0

Reorder the terms:
(-6 + z)(-5 + z) = 0

Multiply (-6 + z) * (-5 + z)
(-6(-5 + z) + z(-5 + z)) = 0
((-5 * -6 + z * -6) + z(-5 + z)) = 0
((30 + -6z) + z(-5 + z)) = 0
(30 + -6z + (-5 * z + z * z)) = 0
(30 + -6z + (-5z + z2)) = 0

Combine like terms: -6z + -5z = -11z
(30 + -11z + z2) = 0

Solving
30 + -11z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
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 = {5, 6}