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

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

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

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

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

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

Combine like terms: -5n + -2n = -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}