(n+4)*(n-5)=112

Solution for (n+4)*(n-5)=112 equation:

Simplifying
(n + 4)(n + -5) = 112

Reorder the terms:
(4 + n)(n + -5) = 112

Reorder the terms:
(4 + n)(-5 + n) = 112

Multiply (4 + n) * (-5 + n)
(4(-5 + n) + n(-5 + n)) = 112
((-5 * 4 + n * 4) + n(-5 + n)) = 112
((-20 + 4n) + n(-5 + n)) = 112
(-20 + 4n + (-5 * n + n * n)) = 112
(-20 + 4n + (-5n + n2)) = 112

Combine like terms: 4n + -5n = -1n
(-20 + -1n + n2) = 112

Solving
-20 + -1n + n2 = 112

Solving for variable 'n'.

Reorder the terms:
-20 + -112 + -1n + n2 = 112 + -112

Combine like terms: -20 + -112 = -132
-132 + -1n + n2 = 112 + -112

Combine like terms: 112 + -112 = 0
-132 + -1n + n2 = 0

Factor a trinomial.
(-11 + -1n)(12 + -1n) = 0

Subproblem 1
Set the factor '(-11 + -1n)' equal to zero and attempt to solve:

Simplifying
-11 + -1n = 0

Solving
-11 + -1n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1n = 0 + 11
-1n = 0 + 11

Combine like terms: 0 + 11 = 11
-1n = 11

Divide each side by '-1'.
n = -11

Simplifying
n = -11
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 = {-11, 12}