-2n^2-11n+144=6

Solution for -2n^2-11n+144=6 equation:

Simplifying
-2n2 + -11n + 144 = 6

Reorder the terms:
144 + -11n + -2n2 = 6

Solving
144 + -11n + -2n2 = 6

Solving for variable 'n'.

Reorder the terms:
144 + -6 + -11n + -2n2 = 6 + -6

Combine like terms: 144 + -6 = 138
138 + -11n + -2n2 = 6 + -6

Combine like terms: 6 + -6 = 0
138 + -11n + -2n2 = 0

Factor a trinomial.
(6 + -1n)(23 + 2n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(23 + 2n)' equal to zero and attempt to solve:

Simplifying
23 + 2n = 0

Solving
23 + 2n = 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 + 2n = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 2n = 0 + -23
2n = 0 + -23

Combine like terms: 0 + -23 = -23
2n = -23

Divide each side by '2'.
n = -11.5

Simplifying
n = -11.5
Solution
n = {6, -11.5}