Question 6099
-15xy-10x
---------
    5x

From -15xy-10x, you can factor out 5x, which leaves -3y-2, which is the solution.
Proof: 5x(-3y-2) = -15xy-10x

2x^2y-6xy^2+12xy
----------------
     2xy

From 2x^2y-6xy^2+12xy, you can factor out 2xy, which leaves:
2x^2y-6xy^2+12xy/2 = x^2y-3xy^2+6xy
x^2y-3xy^2+6xy/x = xy-3y^2+6y
xy-3y^2+6y/y = x-3y+6, which is the solution. (I took it a step at a time to make it easier for me to mentally calculate.)
Proof: 2xy(x-3y+6) = 2x^2y-6xy^2+12xy