Concerning what you've written, I suppose you're trying to solve an algebraic equation of degree 3... something like
ax^3+bx^2+cx+d=0.
Right so far [If not, proceed to[*]]?
I don't know what the 'long division method' is, but it looks as if you know something about one of the polynomial's zeroes.
By using Euclidian division, you can split that zero off the polynomial and as a result, you'll get a polynomial of degree 2.
That would be easy to solve... but for some reason, you don't like it that way
Never mind, if you're looking for a 'closed' formula, you should try to do a search on a guy named 'Gerolamo Cardano' or 'Geroliamo Cardano'.
He's figured out how to solve that kind of stuff.
For a good explanation, take a look at
hxxp://en.wikipedia.org/wiki/Cubic_equation
But... it's not that funny...
[*] Sorry, I've not the slightest idea what's this thread about... I apologize ;-)

Regards
Wurstgote