(n-7)(n+6)=-12

Solution for (n-7)(n+6)=-12 equation:

Simplifying
(n + -7)(n + 6) = -12

Reorder the terms:
(-7 + n)(n + 6) = -12

Reorder the terms:
(-7 + n)(6 + n) = -12

Multiply (-7 + n) * (6 + n)
(-7(6 + n) + n(6 + n)) = -12
((6 * -7 + n * -7) + n(6 + n)) = -12
((-42 + -7n) + n(6 + n)) = -12
(-42 + -7n + (6 * n + n * n)) = -12
(-42 + -7n + (6n + n2)) = -12

Combine like terms: -7n + 6n = -1n
(-42 + -1n + n2) = -12

Solving
-42 + -1n + n2 = -12

Solving for variable 'n'.

Reorder the terms:
-42 + 12 + -1n + n2 = -12 + 12

Combine like terms: -42 + 12 = -30
-30 + -1n + n2 = -12 + 12

Combine like terms: -12 + 12 = 0
-30 + -1n + n2 = 0

Factor a trinomial.
(-5 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
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 = {-5, 6}