I am getting -14 and -4.
has 2 real solutions and two non-real. Are you sure you typed it correctly. One sign is wrong then it's all wrong.
If you factor
As you can see, two soluitons are 3/2 and -1/2
Plug these into the quartic and you get:
Solve these two for p and q and you get q=-14 and p=-4
Sub those in and you get:
The factorization you said was in the book when expanded gives: