I agree with Chris Rogers that the best and right (and long-term reliable) way to fix it is to replace the shell. There is a lot of stress on the hinges and it is tough to do a repair that will have the original strength and hold up long term.
That said, you may not have ready access to a replacement shell and may need at least a temporary repair to keep you operational. Nothing in the way of glue or epoxy will hold up for long by itself, even if it bonds with the plastic. Here's a more robust fix that will last for awhile.
Gorrila Glue or Super glue wouldn't be good for this. Something like JB Weld would have good strength and bond well, but still not close to the original strength. I would go farther. Where those brass insert were, drill a screw clearance hole through case. Get longer screws with matching threads. Glue the brass inserts back in place and use enough JB Weld to provide some support to the insert and the surrounding plastic. Then screw into and through the inserts and through the case. Use a large washer and nut on the outside of the case, with Loctite threadlocker to secure the nut.
That will look ugly, and will probably extend past any case bumpers, so it will have the potential to scratch your furniture. You could cover it with a thin layer of silicone rubber to hide it and protect surfaces (there is black silicone adhesive or gray silicone caulk, or Sugru or Oogoo, if you want a "stylish" repair). Be gentle with sliding the laptop around because that will likely tear off the silicone or erase it, and you would need to replace it.