(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 = -14n
(48 + -14n + n2) = 0

Solving
48 + -14n + 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}