The most common and most likely answer to this crossword clue is the 5 plus 2 letter word AGREE ON
I've seen this crossword clue in Financial Times
A
G
R
E
E
O
N
Buddy explains!
The straight part
We know that "Come to mutually satisfactory solution" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case come to mutually satisfactory solution = agree on.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.