(n-2)(n-5)=0

Solution for (n-2)(n-5)=0 equation:

Simplifying
(n + -2)(n + -5) = 0

Reorder the terms:
(-2 + n)(n + -5) = 0

Reorder the terms:
(-2 + n)(-5 + n) = 0

Multiply (-2 + n) * (-5 + n)
(-2(-5 + n) + n(-5 + n)) = 0
((-5 * -2 + n * -2) + n(-5 + n)) = 0
((10 + -2n) + n(-5 + n)) = 0
(10 + -2n + (-5 * n + n * n)) = 0
(10 + -2n + (-5n + n2)) = 0

Combine like terms: -2n + -5n = -7n
(10 + -7n + n2) = 0

Solving
10 + -7n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(2 + -1n)(5 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
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 = {2, 5}