The hinges that allow a laptop screen to pivot can work themselves loose over time. Asus laptops have hinges that are screwed into place with bolts that go into threaded metal inserts. The inserts are contained in plastic holders which are part of the laptop's casing. The plastic holders are prone to cracking and shearing.
Step 1: Open the Laptop and Fix the Plastic Holders in Place With a Strong Adhesive
Open the laptop carefully (with the help of a youtube disassembly video or other instructions). Unscrew the screen hinges. Cover the metal inserts and their plastic holders with a polymer based construction adhesive or other suitable adhesive.
Make a notch by pushing the hinge into the polymer dispersion adhesive. Take the hinge out and clean it. Remove the threaded metal inserts and their screws. Drill 3mm holes through the laptop's casing where the metal inserts were before.
Step 2: Bolt the Hinges Down Through the Laptop's Casing
Drill the left and right screw holes of both hinges with a 3mm drill bit. Bolt down the hinges through the casing with a 3mm bolt and some washers.
Step 3: Cut the Bolt Tops Off and File Down the Sharp Edges
Use a small metal hacksaw to cut the bolts right above the nuts. File down the bolts.