109=n^2-2n-11

Solution for 109=n^2-2n-11 equation:

Simplifying
109 = n2 + -2n + -11

Reorder the terms:
109 = -11 + -2n + n2

Solving
109 = -11 + -2n + n2

Solving for variable 'n'.

Combine like terms: 109 + 11 = 120
120 + 2n + -1n2 = -11 + -2n + n2 + 11 + 2n + -1n2

Reorder the terms:
120 + 2n + -1n2 = -11 + 11 + -2n + 2n + n2 + -1n2

Combine like terms: -11 + 11 = 0
120 + 2n + -1n2 = 0 + -2n + 2n + n2 + -1n2
120 + 2n + -1n2 = -2n + 2n + n2 + -1n2

Combine like terms: -2n + 2n = 0
120 + 2n + -1n2 = 0 + n2 + -1n2
120 + 2n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
120 + 2n + -1n2 = 0

Factor a trinomial.
(12 + -1n)(10 + n) = 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 '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 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 + n = 0 + -10

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

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

Simplifying
n = -10
Solution
n = {12, -10}