(n-3)(n-5)=0

Solution for (n-3)(n-5)=0 equation:

Simplifying
(n + -3)(n + -5) = 0

Reorder the terms:
(-3 + n)(n + -5) = 0

Reorder the terms:
(-3 + n)(-5 + n) = 0

Multiply (-3 + n) * (-5 + n)
(-3(-5 + n) + n(-5 + n)) = 0
((-5 * -3 + n * -3) + n(-5 + n)) = 0
((15 + -3n) + n(-5 + n)) = 0
(15 + -3n + (-5 * n + n * n)) = 0
(15 + -3n + (-5n + n2)) = 0

Combine like terms: -3n + -5n = -8n
(15 + -8n + n2) = 0

Solving
15 + -8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
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 = {3, 5}