(n-8)(n+6)=0

Solution for (n-8)(n+6)=0 equation:

Simplifying
(n + -8)(n + 6) = 0

Reorder the terms:
(-8 + n)(n + 6) = 0

Reorder the terms:
(-8 + n)(6 + n) = 0

Multiply (-8 + n) * (6 + n)
(-8(6 + n) + n(6 + n)) = 0
((6 * -8 + n * -8) + n(6 + n)) = 0
((-48 + -8n) + n(6 + n)) = 0
(-48 + -8n + (6 * n + n * n)) = 0
(-48 + -8n + (6n + n2)) = 0

Combine like terms: -8n + 6n = -2n
(-48 + -2n + n2) = 0

Solving
-48 + -2n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
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 = {-6, 8}