You can factor out 3 as a start to make the rest easier.

27x^3-36x^2-33x-6 = 3(9x^3 - 12x^2 - 11x - 2)

Now, let f(x) = 9x^3 - 12x^2 - 11x - 2

Find some factors of -2 and 9 which will make f(x) = 0.

2 seems to fit it well. So, (x - 2) is a factor. Hence, divide 9x^3 - 12x^2 - 11x - 2 by x-2

3(9x^3 - 12x^2 - 11x - 2) = 3(x-2)(9x^2+6x+1)

Now that you have a quadratic, you can finish it :)

Post what you get!