(n+7)(n-1)=48

Solution for (n+7)(n-1)=48 equation:

Simplifying
(n + 7)(n + -1) = 48

Reorder the terms:
(7 + n)(n + -1) = 48

Reorder the terms:
(7 + n)(-1 + n) = 48

Multiply (7 + n) * (-1 + n)
(7(-1 + n) + n(-1 + n)) = 48
((-1 * 7 + n * 7) + n(-1 + n)) = 48
((-7 + 7n) + n(-1 + n)) = 48
(-7 + 7n + (-1 * n + n * n)) = 48
(-7 + 7n + (-1n + n2)) = 48

Combine like terms: 7n + -1n = 6n
(-7 + 6n + n2) = 48

Solving
-7 + 6n + n2 = 48

Solving for variable 'n'.

Reorder the terms:
-7 + -48 + 6n + n2 = 48 + -48

Combine like terms: -7 + -48 = -55
-55 + 6n + n2 = 48 + -48

Combine like terms: 48 + -48 = 0
-55 + 6n + n2 = 0

Factor a trinomial.
(-11 + -1n)(5 + -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 '(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
Solution
n = {-11, 5}