6n^2-n-77=0

Solution for 6n^2-n-77=0 equation:

Simplifying
6n2 + -1n + -77 = 0

Reorder the terms:
-77 + -1n + 6n2 = 0

Solving
-77 + -1n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + -2n)(11 + -3n) = 0

Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve:

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5
Subproblem 2
Set the factor '(11 + -3n)' equal to zero and attempt to solve:

Simplifying
11 + -3n = 0

Solving
11 + -3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3n = 0 + -11
-3n = 0 + -11

Combine like terms: 0 + -11 = -11
-3n = -11

Divide each side by '-3'.
n = 3.666666667

Simplifying
n = 3.666666667
Solution
n = {-3.5, 3.666666667}