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

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

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

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

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

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

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

Solving
-40 + -3n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-5, 8}