5n^2-2n-109=6

Solution for 5n^2-2n-109=6 equation:

Simplifying
5n2 + -2n + -109 = 6

Reorder the terms:
-109 + -2n + 5n2 = 6

Solving
-109 + -2n + 5n2 = 6

Solving for variable 'n'.

Reorder the terms:
-109 + -6 + -2n + 5n2 = 6 + -6

Combine like terms: -109 + -6 = -115
-115 + -2n + 5n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-115 + -2n + 5n2 = 0

Factor a trinomial.
(-23 + -5n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-23 + -5n)' equal to zero and attempt to solve:

Simplifying
-23 + -5n = 0

Solving
-23 + -5n = 0

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

Add '23' to each side of the equation.
-23 + 23 + -5n = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -5n = 0 + 23
-5n = 0 + 23

Combine like terms: 0 + 23 = 23
-5n = 23

Divide each side by '-5'.
n = -4.6

Simplifying
n = -4.6
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-4.6, 5}