(n-4)(n-5)=0

Solution for (n-4)(n-5)=0 equation:

Simplifying
(n + -4)(n + -5) = 0

Reorder the terms:
(-4 + n)(n + -5) = 0

Reorder the terms:
(-4 + n)(-5 + n) = 0

Multiply (-4 + n) * (-5 + n)
(-4(-5 + n) + n(-5 + n)) = 0
((-5 * -4 + n * -4) + n(-5 + n)) = 0
((20 + -4n) + n(-5 + n)) = 0
(20 + -4n + (-5 * n + n * n)) = 0
(20 + -4n + (-5n + n2)) = 0

Combine like terms: -4n + -5n = -9n
(20 + -9n + n2) = 0

Solving
20 + -9n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(4 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
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
Solution
n = {4, 5}