8n^2+27n+9=0

Solution for 8n^2+27n+9=0 equation:

Simplifying
8n2 + 27n + 9 = 0

Reorder the terms:
9 + 27n + 8n2 = 0

Solving
9 + 27n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(3 + 8n) = 0

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

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

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

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

Simplifying
n = -3
Subproblem 2
Set the factor '(3 + 8n)' equal to zero and attempt to solve:

Simplifying
3 + 8n = 0

Solving
3 + 8n = 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 + 8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8n = 0 + -3
8n = 0 + -3

Combine like terms: 0 + -3 = -3
8n = -3

Divide each side by '8'.
n = -0.375

Simplifying
n = -0.375
Solution
n = {-3, -0.375}