You can also buy a special glue from your LFS, made especially for putting tank backgrounds on and not showing any white residue. Various brands and roughly about £3-£5 in cost.
Something else you could consider is painting the outside of the back of the tank. I painted mine black to bring out the colors of the fish and the plants. It is however a little more time consuming though. They also make some stick on backgrounds that you just peel off the white paper and stick it to the back outside the tank without needing extra tape.
All I did was take a spray bottle with water, completely wet the poster (as long as it was one of those plastic laminated backgrounds) and worked from the bottom to the top with a cloth getting all the air bubbles out till it was totally flat and just used magic tape to tape the edges down.
Back in the day when I used picture backgrounds I found it much better to use special double sided tabs that you can use on the INSIDE of the tank so the picture was super clear with no bubbles spoiling the look.
1.) Simply attach it with cellotape
2.) Drench the background in water then attach it to the tank with tape. This will make the tank more vibrant.
3.) Apply vasaline to the back of the tank, then apply the background and remove airbubbles.
4.} " Olive Oil "
5.) Paint the back of the tank