Factorisation, please help!!!

Factor the following:
8 x y+2 z (8 x-3 y)-12 z^2

The factors of -96 x y that sum to 2 (8 x-3 y) are -6 y z and 16 x z.
So, -12 z^2+2 (8 x-3 y) z+8 x y = -12 z^2-6 y z+16 x z+8 x y:
-12 z^2-6 y z+16 x z+8 x y

-12 z^2-6 y z+16 x z+8 x y = 4 z (4 x-3 z)+2 y (4 x-3 z):
4 z (4 x-3 z)+2 y (4 x-3 z)

Factor 4 x-3 z out of 4 z (4 x-3 z)+2 y (4 x-3 z), resulting in (4 x-3 z) (4 z+2 y):
(4 x-3 z) (4 z+2 y)

Factor 2 out of 4 z+2 y:
Answer: |  2 (2 z+y) (4 x-3 z)

8 x y+2 z (8 x-3 y)-12 z^2    expand

8xy + 16zx - 6yz - 12z^2   factor

8x(y + 2z) - 6z(y + 2z)

(y + 2z) (8x - 6z)

(y + 2z) * 2 (4x - 3z)  =

2(y + 2z)(4x - 3z)