6n^2=-240+78n

Solution for 6n^2=-240+78n equation:

Simplifying
6n2 = -240 + 78n

Solving
6n2 = -240 + 78n

Solving for variable 'n'.

Reorder the terms:
240 + -78n + 6n2 = -240 + 78n + 240 + -78n

Reorder the terms:
240 + -78n + 6n2 = -240 + 240 + 78n + -78n

Combine like terms: -240 + 240 = 0
240 + -78n + 6n2 = 0 + 78n + -78n
240 + -78n + 6n2 = 78n + -78n

Combine like terms: 78n + -78n = 0
240 + -78n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(40 + -13n + n2) = 0

Factor a trinomial.
6((5 + -1n)(8 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
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 = {5, 8}