Hi, if you cut the edges of the hole at a sharp outward angle, cut a scrap piece of sheetrock in a matching size to fit the hole, angle the edges of the patch piece – keep trying the patch for compatibility – you will be able to mud in the patch so it is unnoticeable. This works for holes up to about 6″.
I have done this repair many times. It can be used for small holes as well as larger holes
Place a peice of wood about two inches bigger than the hole in side the hole behind the sheet (sheep) rock. You secure the wood to the sheetrock by screwing a couple of screws on each end through the existing sheetrock and into the wood. This will hold the wood in place behind the hole so that a peice of sheetrock can be secred to the wood. The hole is now closed. Apply joint compound, paper tape then sand in between joint compund coats paint it and pass this tip on to others. Bob
I once had a similar problem near a door. We had tried to move a sofa out the door without taking the door off the hinges. The sofa pushed the doorknob into the wall resulting in this huge hole in the sheetrock. I saw in a mail-order catalog a solution for this very problem: their product was a round plastic thing that was indented inward. You install in in the wall, even with a doorknob, and it keeps the doorknob from making a place in the wall. I am not a handyman at all, but I already had the hole in the right location, so I sent for this item. I was able to install it and it looks great! If I can do it, anyone can. Sorry I don’t recall the name of the catalog. It also may be available in a hardware store or Lowe’s or Home Depot….