Solve for x:
9 + 27/x + 8/x^2 = 0
Bring 9 + 27/x + 8/x^2 together using the common denominator x^2:
(9 x^2 + 27 x + 8)/x^2 = 0
Multiply both sides by x^2:
9 x^2 + 27 x + 8 = 0
The left hand side factors into a product with two terms:
(3 x + 1) (3 x + 8) = 0
Split into two equations:
3 x + 1 = 0 or 3 x + 8 = 0
Subtract 1 from both sides:
3 x = -1 or 3 x + 8 = 0
Divide both sides by 3:
x = -1/3 or 3 x + 8 = 0
Subtract 8 from both sides:
x = -1/3 or 3 x = -8
Divide both sides by 3:
x = -1/3 or x = -8/3