14n^2+39n+27=0

Solution for 14n^2+39n+27=0 equation:

Simplifying
14n2 + 39n + 27 = 0

Reorder the terms:
27 + 39n + 14n2 = 0

Solving
27 + 39n + 14n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + 2n)(9 + 7n) = 0

Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(9 + 7n)' equal to zero and attempt to solve:

Simplifying
9 + 7n = 0

Solving
9 + 7n = 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 + 7n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7n = 0 + -9
7n = 0 + -9

Combine like terms: 0 + -9 = -9
7n = -9

Divide each side by '7'.
n = -1.285714286

Simplifying
n = -1.285714286
Solution
n = {-1.5, -1.285714286}