110=n(n+1)

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

Simplifying
110 = n(n + 1)

Reorder the terms:
110 = n(1 + n)
110 = (1 * n + n * n)
110 = (1n + n2)

Solving
110 = 1n + n2

Solving for variable 'n'.

Reorder the terms:
110 + -1n + -1n2 = 1n + -1n + n2 + -1n2

Combine like terms: 1n + -1n = 0
110 + -1n + -1n2 = 0 + n2 + -1n2
110 + -1n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
110 + -1n + -1n2 = 0

Factor a trinomial.
(10 + -1n)(11 + n) = 0

Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
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 = {10, -11}