6n^2+84n+270=0

Solution for 6n^2+84n+270=0 equation:

Simplifying
6n2 + 84n + 270 = 0

Reorder the terms:
270 + 84n + 6n2 = 0

Solving
270 + 84n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(45 + 14n + n2) = 0

Factor a trinomial.
6((9 + n)(5 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 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 + n = 0 + -5

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

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

Simplifying
n = -5
Solution
n = {-9, -5}