6n^2-5n-344=0

Solution for 6n^2-5n-344=0 equation:

Simplifying
6n2 + -5n + -344 = 0

Reorder the terms:
-344 + -5n + 6n2 = 0

Solving
-344 + -5n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-43 + -6n)(8 + -1n) = 0

Subproblem 1
Set the factor '(-43 + -6n)' equal to zero and attempt to solve:

Simplifying
-43 + -6n = 0

Solving
-43 + -6n = 0

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

Add '43' to each side of the equation.
-43 + 43 + -6n = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -6n = 0 + 43
-6n = 0 + 43

Combine like terms: 0 + 43 = 43
-6n = 43

Divide each side by '-6'.
n = -7.166666667

Simplifying
n = -7.166666667
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-7.166666667, 8}