(n+1)(n-5)=16

Solution for (n+1)(n-5)=16 equation:

Simplifying
(n + 1)(n + -5) = 16

Reorder the terms:
(1 + n)(n + -5) = 16

Reorder the terms:
(1 + n)(-5 + n) = 16

Multiply (1 + n) * (-5 + n)
(1(-5 + n) + n(-5 + n)) = 16
((-5 * 1 + n * 1) + n(-5 + n)) = 16
((-5 + 1n) + n(-5 + n)) = 16
(-5 + 1n + (-5 * n + n * n)) = 16
(-5 + 1n + (-5n + n2)) = 16

Combine like terms: 1n + -5n = -4n
(-5 + -4n + n2) = 16

Solving
-5 + -4n + n2 = 16

Solving for variable 'n'.

Reorder the terms:
-5 + -16 + -4n + n2 = 16 + -16

Combine like terms: -5 + -16 = -21
-21 + -4n + n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-21 + -4n + n2 = 0

Factor a trinomial.
(-3 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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 = {-3, 7}