"tear apart" or "rip apart" packaging?
Solution 1:
If you don't intend to say that you opened the package rather savagely, I would suggest using "tore open the package".
E.g:
I tore open the package only to be disappointed by what I found inside.
The choice of the phrase "rip apart" suggests the package was opened in a fierce and savage manner, probably destroying the packing material in the process.
E.g:
I had been waiting for the package to arrive all week and ripped the cover apart as soon as I got my hands on it.
As an added note I would like to mention that both the choices do suggest that the packing material/wrapper was damaged during unpacking. However, "cutting open" the package would mean that the entire operation was carried out in a sophisticated and careful manner.