(n+2)(n-8)=0

Solution for (n+2)(n-8)=0 equation:

Simplifying
(n + 2)(n + -8) = 0

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

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

Multiply (2 + n) * (-8 + n)
(2(-8 + n) + n(-8 + n)) = 0
((-8 * 2 + n * 2) + n(-8 + n)) = 0
((-16 + 2n) + n(-8 + n)) = 0
(-16 + 2n + (-8 * n + n * n)) = 0
(-16 + 2n + (-8n + n2)) = 0

Combine like terms: 2n + -8n = -6n
(-16 + -6n + n2) = 0

Solving
-16 + -6n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -1n)(8 + -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 '(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 = {-2, 8}