"a shared room"
"Совместо" is not a word in Russian. If you meant "совместно" then it's an adwerb not an adjective, so it cant be used in place of the adjective "общая". You could rephrase the sentence and say "комната, которой мы владеем совместно" - "a room that we own together", but that's a rather unnecessary complicated way to express this thought.
I'm sorry I should have acknowledged your previous message I think you answered some days ago? I accepted what you said and that the correct way to say a shared room is общая комната. I think I answered that way to see whether or not it would be correct. I am not sure about the word order for adjectives whether as in English they mostly go before the noun or as in French they go afterwards with some exceptions. Presumably in this case the meaning is the same it is my translation which is incorrect?