6x^3 - 21x^2 + 9x
The first rule in factoring is to take out the greatest common factor, i.e., 3......so we have
3(2x^3 - 7x +3)......now forget the 3, we'll add it back later
So. let's see if we can factor (2x^3 - 7x +3)
We need to find something that multiplies to 2 (the first coefficient) and something else that multiplies to 3 (the last coefficient). The final goal is that the sum of these two products should equal the middle coefficient, (-7). Trial and error is the way to go here.
Let's try.... (2x + 1) (x + 3)....Nope.....I get a (+ 7x) and I need a (-7x)
Mmmmm...we're close !!! Since I know that (-3) * (-1) also gives me a (+3), let's try that.
(2x - 1) (x - 3)......Hey, this gives us what we need !!!
Now, go back and "stick" the "3" on the front.....So we have
3(2x - 1) (x - 3)
And that's it !!
+130466 
