(n-6)(n-4)=0

Solution for (n-6)(n-4)=0 equation:

Simplifying
(n + -6)(n + -4) = 0

Reorder the terms:
(-6 + n)(n + -4) = 0

Reorder the terms:
(-6 + n)(-4 + n) = 0

Multiply (-6 + n) * (-4 + n)
(-6(-4 + n) + n(-4 + n)) = 0
((-4 * -6 + n * -6) + n(-4 + n)) = 0
((24 + -6n) + n(-4 + n)) = 0
(24 + -6n + (-4 * n + n * n)) = 0
(24 + -6n + (-4n + n2)) = 0

Combine like terms: -6n + -4n = -10n
(24 + -10n + n2) = 0

Solving
24 + -10n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(4 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
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
Solution
n = {4, 6}