We need to understand that the sign of your constant )that's your number -27) dictates how you factor. A + and - number multipled together yields a - number.
The middle term dictates what number is asigned the + or - signs. Knowing that are 6 is positive, the larger number will be assigned the positive sign.
So what to numbers multiply together to yield- 27, but have a difference of +6. +9 x -3 = -27
Therefore, we break our binomial up as follows, (x+9)(x-3)