(n-1)(n-5)=0

Solution for (n-1)(n-5)=0 equation:

Simplifying
(n + -1)(n + -5) = 0

Reorder the terms:
(-1 + n)(n + -5) = 0

Reorder the terms:
(-1 + n)(-5 + n) = 0

Multiply (-1 + n) * (-5 + n)
(-1(-5 + n) + n(-5 + n)) = 0
((-5 * -1 + n * -1) + n(-5 + n)) = 0
((5 + -1n) + n(-5 + n)) = 0
(5 + -1n + (-5 * n + n * n)) = 0
(5 + -1n + (-5n + n2)) = 0

Combine like terms: -1n + -5n = -6n
(5 + -6n + n2) = 0

Solving
5 + -6n + n2 = 0

Solving for variable 'n'.

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
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 = {1, 5}