(n-5)(n+8)=0

Solution for (n-5)(n+8)=0 equation:

Simplifying
(n + -5)(n + 8) = 0

Reorder the terms:
(-5 + n)(n + 8) = 0

Reorder the terms:
(-5 + n)(8 + n) = 0

Multiply (-5 + n) * (8 + n)
(-5(8 + n) + n(8 + n)) = 0
((8 * -5 + n * -5) + n(8 + n)) = 0
((-40 + -5n) + n(8 + n)) = 0
(-40 + -5n + (8 * n + n * n)) = 0
(-40 + -5n + (8n + n2)) = 0

Combine like terms: -5n + 8n = 3n
(-40 + 3n + n2) = 0

Solving
-40 + 3n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
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 = {-8, 5}