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.
(-10 + -1n)(11 + -1n) = 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 + -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
Solution
n = {-10, 11}