(1+n)(2+n)=110

Solution for (1+n)(2+n)=110 equation:

Simplifying
(1 + n)(2 + n) = 110

Multiply (1 + n) * (2 + n)
(1(2 + n) + n(2 + n)) = 110
((2 * 1 + n * 1) + n(2 + n)) = 110
((2 + 1n) + n(2 + n)) = 110
(2 + 1n + (2 * n + n * n)) = 110
(2 + 1n + (2n + n2)) = 110

Combine like terms: 1n + 2n = 3n
(2 + 3n + n2) = 110

Solving
2 + 3n + n2 = 110

Solving for variable 'n'.

Reorder the terms:
2 + -110 + 3n + n2 = 110 + -110

Combine like terms: 2 + -110 = -108
-108 + 3n + n2 = 110 + -110

Combine like terms: 110 + -110 = 0
-108 + 3n + n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-12, 9}