Billy shelves wobbly problem

Before fixing, the back piece of the shelve was wobbly and impossible to stay in place. 

After adding brackets to the top and bottom, nailing nails at new position behind the bottom of the shelve, I think it should not have the wobbly problem anymore.

All I need to do is buy glue, unscrew, add glue, screw back, and paint the shelves. I have got 3 short billy shelves waiting for me to do just that. Another 3 tall billy to be fixed without painting. Lots of work around the house.