Cryptic crossword clue
Agonising to keep solving algebra, agreeing to a lesser punishment 4,10

The most common and most likely answer to this crossword clue is the 4 plus 10 letter word PLEA BARGAINING

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Buddy explains!

The straight part
We know that "agreeing to a lesser punishment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case agreeing to a lesser punishment = plea bargaining.
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.

What does PLEA BARGAINING mean?

PLEA BARGAINING verb
  1. To make an agreement in which a defendant agrees to plead guilty to a lesser charge instead of not guilty to a greater one.

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