Factor the following:

-4 y^2 + 3 x y - 12 y + 9 x

Factor terms by grouping. -4 y^2 + 3 x y - 12 y + 9 x = (3 x y - 4 y^2) + (9 x - 12 y) = y (3 x - 4 y) + 3 (3 x - 4 y):

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

Factor 3 x - 4 y from y (3 x - 4 y) + 3 (3 x - 4 y):

**=(3x - 4y) (y + 3)**