Eftir langt samtal náðum við samkomulagi um að skipta kostnaðinum jafnt.

This is because Icelandic is a V2 language in main clauses: the finite verb normally comes second.

Here, the sentence starts with Eftir langt samtal. That whole phrase takes the first position, so the finite verb náðum has to come next, and the subject við follows it:

Eftir langt samtal | náðum | við ...

If you started the sentence with the subject instead, then you would say:

Við náðum samkomulagi ...

Both are correct; the word order changes because of the V2 rule.

Here eftir means after in a time sense, and in that use it takes the accusative.

So samtal must be in the accusative singular. Since samtal is a neuter noun, the adjective langur has to agree with it, giving:

• langt = accusative singular neuter
• samtal = accusative singular neuter

So:

eftir langt samtal = after a long conversation

Because samtal is a neuter noun.

Icelandic adjectives must agree with the noun in:

• gender
• number
• case

The noun samtal is:

• neuter
• singular
• accusative here, because of eftir

So the adjective must also be neuter singular accusative, which gives langt.

A form like langan would be used with a masculine noun, not a neuter one.

Náðum is the 1st person plural past tense of ná.

So:

• ná = to reach, achieve, manage to
• náðum = we reached / we achieved

The ending -um shows we in the past tense here.

Because the verb ná often takes a dative object when it means reach / achieve something.

The noun is:

• samkomulag = agreement

Its dative singular form is:

• samkomulagi

So:

ná samkomulagi = reach an agreement

This is a very common Icelandic expression.

Because the sentence is talking about reaching an agreement, not the specific agreement.

So Icelandic uses the indefinite noun:

• samkomulagi = an agreement / agreement

If you wanted to refer to a specific, already known agreement, you could use the definite form:

• samkomulaginu = the agreement

In this sentence, the indefinite form is the natural choice.

In this sentence, um að + infinitive expresses what the agreement was about or what the people agreed to do.

So:

samkomulag um að skipta kostnaðinum jafnt

means roughly:

an agreement to divide the cost equally

Here:

• um goes with samkomulag
• að introduces the infinitive skipta

This is a very common pattern in Icelandic:

• samkomulag um að gera eitthvað = agreement to do something

Because skipta, when it means divide / split / apportion, commonly takes the thing being divided in the dative.

So:

• kostnaður = cost, expense
• kostnaðinum = the cost (dative singular definite)

That is why the sentence says:

skipta kostnaðinum jafnt

= divide the cost equally

Yes:

The dictionary form is:

• kostnaður = cost, expense

This is a masculine noun. In oblique cases, the stem changes to kostnað-.

So:

• nominative singular: kostnaður
• dative singular: kostnaði
• dative singular definite: kostnaðinum

The ending -num is part of the suffixed definite article in this case form, so kostnaðinum means the cost.

Here jafnt is being used adverbially, and it means equally or evenly.

It comes from the adjective jafn = equal, even. In Icelandic, the neuter singular form of an adjective is often used like an adverb.

So:

skipta kostnaðinum jafnt
= divide the cost equally

This is completely normal Icelandic usage.

Yes, it is a very common expression meaning reach an agreement.

Learners often meet it as a set phrase:

• ná samkomulagi

Another very common Icelandic expression with almost the same meaning is:

• komast að samkomulagi = come to an agreement

So the sentence sounds very natural, and ná samkomulagi is worth learning as a chunk.

Yes. You could say:

Við náðum samkomulagi um að skipta kostnaðinum jafnt eftir langt samtal.

That is grammatically possible. But when Eftir langt samtal is placed at the front, it gives that time/background information more prominence.

So the original sentence is natural because it sets the scene first: After a long conversation, we reached an agreement...