Learn French: Ils négociaient cet arrangement depuis un mois. - They had been negotiating this settlement for a month.

In French, when an action started in the past and was still ongoing at a specific past moment, you use the imparfait with depuis. English uses the past perfect continuous ("had been doing"). If you translated this literally into the plus-que-parfait (ils avaient négocié), it would mean the negotiation had completely finished before the past moment you are talking about, which changes the meaning.

Why use depuis here instead of pendant for "for a month"?

You use depuis because the negotiation was still actively happening at the time of the story. If you used pendant un mois, it would mean the negotiation lasted for exactly one month as a completed, closed block of time in the past (and you would typically use the passé composé: ils ont négocié pendant un mois).

Verbs with a soft "c" often need a cedilla (ç) before an "a". Why is there no cedilla in négociaient?

The infinitive is négocier. To form the imparfait, you take the stem from the present nous form (négocions), which gives you the stem négoci-. You then add the imparfait ending -aient. Because the c is directly followed by an i, it naturally makes a soft "s" sound. You only need a cedilla when a c is directly followed by a, o, or u (as in ils commençaient).

Can arrangement mean something more specific than just organizing things?