quadratic formula problem

Hi, I'm actually in a college precal2 class, but I think this is an alegbra issue...

I'm sure I'm just being an idiot and doing something completely stupid here, as I haven't taken a math class in over a year and have forgotten everything, but this is my problem:

When working on factoring something for a rational function problem, I can't seem to get the quadratic formula to work out properly.

ex. f(x)= -x^2 - x + 6

y= ( 1 +or- sqrt( -1^2 - 4(-1)(6) ) / 2(=1)

solving this gets me y= -3 or 2

which means the factors are (x+3)(x-2), right? But then multiplying those back together gets x^2 + x - 6, which is the same as the start, but with all the signs flipped... am I suppposed to be putting a negative out front, like -(x+3)(x-2)? I'm really confused... does this also mean that if the original function was something like 2x^2 - x +6, I'd need to put a 2 somewhere? I don't get it, and can't remember what I'm supposed to do...

I'm sure this is just a stupid simple mistake, but I'd really like some help, I'm just frustrating myself at the moment.... Thanks!