n+n+2+n+4=(n+2)(n+4)-110

Solution for n+n+2+n+4=(n+2)(n+4)-110 equation:

Simplifying
n + n + 2 + n + 4 = (n + 2)(n + 4) + -110

Reorder the terms:
2 + 4 + n + n + n = (n + 2)(n + 4) + -110

Combine like terms: 2 + 4 = 6
6 + n + n + n = (n + 2)(n + 4) + -110

Combine like terms: n + n = 2n
6 + 2n + n = (n + 2)(n + 4) + -110

Combine like terms: 2n + n = 3n
6 + 3n = (n + 2)(n + 4) + -110

Reorder the terms:
6 + 3n = (2 + n)(n + 4) + -110

Reorder the terms:
6 + 3n = (2 + n)(4 + n) + -110

Multiply (2 + n) * (4 + n)
6 + 3n = (2(4 + n) + n(4 + n)) + -110
6 + 3n = ((4 * 2 + n * 2) + n(4 + n)) + -110
6 + 3n = ((8 + 2n) + n(4 + n)) + -110
6 + 3n = (8 + 2n + (4 * n + n * n)) + -110
6 + 3n = (8 + 2n + (4n + n2)) + -110

Combine like terms: 2n + 4n = 6n
6 + 3n = (8 + 6n + n2) + -110

Reorder the terms:
6 + 3n = 8 + -110 + 6n + n2

Combine like terms: 8 + -110 = -102
6 + 3n = -102 + 6n + n2

Solving
6 + 3n = -102 + 6n + n2

Solving for variable 'n'.

Reorder the terms:
6 + 102 + 3n + -6n + -1n2 = -102 + 6n + n2 + 102 + -6n + -1n2

Combine like terms: 6 + 102 = 108
108 + 3n + -6n + -1n2 = -102 + 6n + n2 + 102 + -6n + -1n2

Combine like terms: 3n + -6n = -3n
108 + -3n + -1n2 = -102 + 6n + n2 + 102 + -6n + -1n2

Reorder the terms:
108 + -3n + -1n2 = -102 + 102 + 6n + -6n + n2 + -1n2

Combine like terms: -102 + 102 = 0
108 + -3n + -1n2 = 0 + 6n + -6n + n2 + -1n2
108 + -3n + -1n2 = 6n + -6n + n2 + -1n2

Combine like terms: 6n + -6n = 0
108 + -3n + -1n2 = 0 + n2 + -1n2
108 + -3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
108 + -3n + -1n2 = 0

Factor a trinomial.
(9 + -1n)(12 + n) = 0

Subproblem 1
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Subproblem 2
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 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 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
Solution
n = {9, -12}