Just a heads up. I read this little post on XDA and another user's resolution was:
-Go to Settings->Applications->Manage Applications->All
-Select "Clear Data" for Google Play Services and Google Service Framework
-Reboot the device
This would be a good first start. I did some more digging (as I am unable to recreate the fault) and found it also appears necessary to remove your Google Account and re-add it to your device, so this may also be a good shot.
If this is a dire circumstance (and you cannot format your phone or perform a system update), you can enable unknown sources and find the APK you need - this should install.
Lastly, here is a nice little video to help demonstrate what you need to do.
[RPC:S-7:AEC-7 QNHM-TYSO-UNVHY]
; error codes list in our google-play-store tag-wiki updated). – Izzy♦ Feb 10 '16 at 12:17