I added a 1-inch flat board behind the TV that went across the wall. You want to at least pull a larger outside board up against the small studs inside the wall for support. Once you trim and paint it looks real nice... If you can't screw the four corners of this large backboard into the wall studs then use what is called MOLLY BOLTS that spread out on the inside of the wall to keep from being pulled through the screw hole...
40-inch TV is a pretty good size but is very light compared to the old heavy analog type TVs...
Here are a couple of ideas from GOOGLE SEARCH
As noted above the mounting hardware all attaches to the back of the TV standard mounting bolts. Read the specs on the mounts and get one that will support the weight of the mounted TV set. Anther feature you probably want to get is find a mount that tilts down as well as left to right. ALot of the LCD TVs don't do well unless you are viewing directly into the screen. You also should get the best mounting adapter that will easily disconnect if you want to remove the TV SET without removing alot of screws. My mount has a pivot bolt that uses a clip and then you just lift up on oit to remove it...
WALMART has a lot of these mounts on display...
For me the MOLLY BOLTS was best to use to mount the BACKBOARD wood as they stay attached to the wall unlike the other popular wing type mounting. The wing type will drop the spring loaded nut behind the wall if you unscrew the mounting bolts...
Roy Ken