6n^2+5n-144=0

Solution for 6n^2+5n-144=0 equation:

Simplifying
6n2 + 5n + -144 = 0

Reorder the terms:
-144 + 5n + 6n2 = 0

Solving
-144 + 5n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-16 + -3n)(9 + -2n) = 0

Subproblem 1
Set the factor '(-16 + -3n)' equal to zero and attempt to solve:

Simplifying
-16 + -3n = 0

Solving
-16 + -3n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3n = 0 + 16
-3n = 0 + 16

Combine like terms: 0 + 16 = 16
-3n = 16

Divide each side by '-3'.
n = -5.333333333

Simplifying
n = -5.333333333
Subproblem 2
Set the factor '(9 + -2n)' equal to zero and attempt to solve:

Simplifying
9 + -2n = 0

Solving
9 + -2n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2n = 0 + -9
-2n = 0 + -9

Combine like terms: 0 + -9 = -9
-2n = -9

Divide each side by '-2'.
n = 4.5

Simplifying
n = 4.5
Solution
n = {-5.333333333, 4.5}