(n-6)(n-5)=0

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

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

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

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

Multiply (-6 + n) * (-5 + n)
(-6(-5 + n) + n(-5 + n)) = 0
((-5 * -6 + n * -6) + n(-5 + n)) = 0
((30 + -6n) + n(-5 + n)) = 0
(30 + -6n + (-5 * n + n * n)) = 0
(30 + -6n + (-5n + n2)) = 0

Combine like terms: -6n + -5n = -11n
(30 + -11n + n2) = 0

Solving
30 + -11n + n2 = 0

Solving for variable 'n'.

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

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

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

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

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

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

Simplifying
n = 5
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

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

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

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

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

Simplifying
n = 6
Solution
n = {5, 6}