(n-7)(n-6)=0

Solution for (n-7)(n-6)=0 equation:

Simplifying
(n + -7)(n + -6) = 0

Reorder the terms:
(-7 + n)(n + -6) = 0

Reorder the terms:
(-7 + n)(-6 + n) = 0

Multiply (-7 + n) * (-6 + n)
(-7(-6 + n) + n(-6 + n)) = 0
((-6 * -7 + n * -7) + n(-6 + n)) = 0
((42 + -7n) + n(-6 + n)) = 0
(42 + -7n + (-6 * n + n * n)) = 0
(42 + -7n + (-6n + n2)) = 0

Combine like terms: -7n + -6n = -13n
(42 + -13n + n2) = 0

Solving
42 + -13n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + -1n)(7 + -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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {6, 7}