n(n+1)=110

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

Simplifying
n(n + 1) = 110

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

Solving
1n + n2 = 110

Solving for variable 'n'.

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

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

Factor a trinomial.
(-11 + -1n)(10 + -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 '(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
Solution
n = {-11, 10}