(n-6)(n-12)=

Solution for (n-6)(n-12)= equation:

Simplifying
(n + -6)(n + -12) = 0

Reorder the terms:
(-6 + n)(n + -12) = 0

Reorder the terms:
(-6 + n)(-12 + n) = 0

Multiply (-6 + n) * (-12 + n)
(-6(-12 + n) + n(-12 + n)) = 0
((-12 * -6 + n * -6) + n(-12 + n)) = 0
((72 + -6n) + n(-12 + n)) = 0
(72 + -6n + (-12 * n + n * n)) = 0
(72 + -6n + (-12n + n2)) = 0

Combine like terms: -6n + -12n = -18n
(72 + -18n + n2) = 0

Solving
72 + -18n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + -1n)(12 + -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 '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {6, 12}