6n^2=77-n

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

Simplifying
6n2 = 77 + -1n

Solving
6n2 = 77 + -1n

Solving for variable 'n'.

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

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

Combine like terms: 77 + -77 = 0
-77 + n + 6n2 = 0 + -1n + n
-77 + n + 6n2 = -1n + n

Combine like terms: -1n + n = 0
-77 + n + 6n2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-3.666666667, 3.5}