The most common and most likely answer to this crossword clue is the 15 letter word TRIAL-AND-ERROR
I've seen this crossword clue in The Times
T
R
I
A
L
-
A
N
D
-
E
R
R
O
R
Buddy explains!
The straight part
We know that "Experimenting until a solution is found" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case experimenting until a solution is found = trial-and-error.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.