Here’s a good example of how many of my household projects turn out. This is the top of a shelving bracket I installed in my garage. To the right of it, you can clearly see the hole in my wall where the original screw pulled out of the sheetrock.
So, I shifted it over about an inch and tried again. That screw pulled out of the sheetrock as well, but I didn’t feel like shifting the bracket over a third time. So, I just cut an L-bracket with my hacksaw and screwed it into the top of the bracket and then into the wall. The screw didn’t pull out of that one.

Ah, a job well done.

Look, there’s a whole wikipedia entry on this type of work!