Empty the bookcase of anything on the shelves. Lift the shelves off the rods extruding from the inside edges of the bookcase. Place the shelves aside. Place the bookcase against the plasterboard wall in the location where you want it to be. Place a ladder against the wall next to the bookcase.
Measure in 2 inches from the back left corner of the bookcase. Place an "L" bracket on the top of the bookcase at the 2-inch mark so that the top of the bracket is up against the wall. Make a dot through the two holes in the side of the "L" bracket that is up against the wall, and in the side of the "L" bracket that is lying on the top of the bookcase -- use a grease pencil for this. Repeat this procedure with the other "L" bracket at the top of the bookcase, starting with a measurement taken 2 inches in from the back right corner.
Remove the "L" brackets and place them aside. Gouge a hole through each of the dots made on the plasterboard wall with the point of a Phillips screwdriver. Place a locking tab screw holder into each of the holes. Push the locking tab screw holder into each of the holes with your fingers until its front is flush with the hole.
Wipe the top of the bookcase with a paper towel moistened in tap water to remove the loose dust from the plasterboard wall. Dry the top of the bookcase with a dry paper towel. Place the two "L" brackets back on the top of the bookcase -- lining up the holes in the brackets with the holes in the wall and the dots on the bookcase.
Screw wood screws through the holes in the "L" brackets that are on the top of the bookcase -- an electric screwdriver will speed up the process if one is available; otherwise, use a Phillips screwdriver.
Push in on the sides of a plastic wall plug to compress the extruding tabs. Place the plastic wall plug into one of the holes in the "L" bracket that is up against the wall. Push the plastic wall plug fully into the hole with your fingers. Repeat this procedure with the other holes in the wall.
Place the shelves back on the bookcase. Return the items that were taken off the shelves earlier to their former positions.