How do you factor 3x squared plus 9x minus 2x minus 6?

3x^(2) +9x - 2x -6

Collect 'like terms'.

Hence

3x^(2) + 7x - 6

Next write down all the factors of '3' and '6'

Hence

3 ; 1' & 3'

6 ; 1,6 ; 2,3.

From these pairs of number we select a pair from each coefficient, that add/multiply to '7' .

Hence

(3' x 3 ) & (1' x 2) ; NB 'dashes' (') to indicate source of numbers.

Write up brackets

(3x 2)(x 3) -2)(x + 3)

Next we notice that the '6' is negative, so the two signs are different (+/-) The '7x' is positive , so the larger number takes the positive sign .

Hence

(3x - 2)(x + 3)