How do you factor

$\displaystyle 18x^3-57x^2-85x+100$ ?

The first thing I tried was grouping:

$\displaystyle 3x(6x^2-19)-5(17x-20)$

That's not going to work, so I tried factoring out an x and then factoring the trinomial. However, I never got past factoring the trinomial...

I've gotten as far as

$\displaystyle x(18x^2-57x-85)+100$

However, I cannot factor the trinomial. I made a list of every possible combination of the factors of 18 and the factors of 85, and their results. None of them added up to -57.

Factors of 18:

$\displaystyle (1,18)(2,9)(3,6)$

Factors of 85:

$\displaystyle (1,-85)(-1,85)(5,-17)(-5,17)$

After that, I made the long list of these sums:

$\displaystyle (1*5)+(18*-17)=+-301$

(I put in the plus/ minus to save time, since switching the negative would change nothing.)

$\displaystyle (1*17)+(18*5)=+-73$

$\displaystyle (1*1)+(18*1)=+-...$

You get it. I went through every possible combination, but never got to a +-57.

So how do I get the answer:

$\displaystyle (x-4) (3x+5) (6x-5)$