n(9n+3)=240

Solution for n(9n+3)=240 equation:

Simplifying
n(9n + 3) = 240

Reorder the terms:
n(3 + 9n) = 240
(3 * n + 9n * n) = 240
(3n + 9n2) = 240

Solving
3n + 9n2 = 240

Solving for variable 'n'.

Reorder the terms:
-240 + 3n + 9n2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 3n + 9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-80 + n + 3n2) = 0

Factor a trinomial.
3((-16 + -3n)(5 + -1n)) = 0

Ignore the factor 3.
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 '(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
Solution
n = {-5.333333333, 5}