108=(n+5)(n-7)

Solution for 108=(n+5)(n-7) equation:

Simplifying
108 = (n + 5)(n + -7)

Reorder the terms:
108 = (5 + n)(n + -7)

Reorder the terms:
108 = (5 + n)(-7 + n)

Multiply (5 + n) * (-7 + n)
108 = (5(-7 + n) + n(-7 + n))
108 = ((-7 * 5 + n * 5) + n(-7 + n))
108 = ((-35 + 5n) + n(-7 + n))
108 = (-35 + 5n + (-7 * n + n * n))
108 = (-35 + 5n + (-7n + n2))

Combine like terms: 5n + -7n = -2n
108 = (-35 + -2n + n2)

Solving
108 = -35 + -2n + n2

Solving for variable 'n'.

Combine like terms: 108 + 35 = 143
143 + 2n + -1n2 = -35 + -2n + n2 + 35 + 2n + -1n2

Reorder the terms:
143 + 2n + -1n2 = -35 + 35 + -2n + 2n + n2 + -1n2

Combine like terms: -35 + 35 = 0
143 + 2n + -1n2 = 0 + -2n + 2n + n2 + -1n2
143 + 2n + -1n2 = -2n + 2n + n2 + -1n2

Combine like terms: -2n + 2n = 0
143 + 2n + -1n2 = 0 + n2 + -1n2
143 + 2n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
143 + 2n + -1n2 = 0

Factor a trinomial.
(13 + -1n)(11 + n) = 0

Subproblem 1
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Subproblem 2
Set the factor '(11 + n)' equal to zero and attempt to solve:

Simplifying
11 + n = 0

Solving
11 + n = 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 + n = 0 + -11

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

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

Simplifying
n = -11
Solution
n = {13, -11}