Det lykkedes os at finde en fælles løsning, selv om vi først var uenige.

Here Det is a dummy/formal subject. Danish often uses this kind of det with verbs like lykkes.

So:

• Det lykkedes os at finde en fælles løsning
  literally: It succeeded for us to find a common solution
• natural English: We managed to find a common solution

So the det is there because Danish grammar wants a subject, even though it does not point to a specific thing.

Lykkedes is the past tense of at lykkes.

In this sentence, at lykkes means:

• to succeed
• to manage to do something

So Det lykkedes os at finde... means We succeeded in finding... or more naturally We managed to find...

Some useful forms:

• det lykkes = it succeeds / we manage
• det lykkedes = it succeeded / we managed
• det er lykkedes = it has succeeded / we have managed

Because os is the object form of we.

Compare:

• vi = we
• os = us

With lykkes, Danish uses the people involved in the object form:

• Det lykkedes mig = I managed
• Det lykkedes dig = you managed
• Det lykkedes os = we managed

So vi would be wrong here.

Because Danish often uses lykkes + someone + at + infinitive to say what was achieved.

Pattern:

• Det lykkedes + person + at + verb

Examples:

• Det lykkedes hende at komme til tiden = She managed to arrive on time
• Det lykkedes os at finde en løsning = We managed to find a solution

So at finde simply tells you what it was that succeeded.

It is a noun phrase:

• en = a
• fælles = common / shared / joint
• løsning = solution

So:

• en fælles løsning = a common/shared solution

Also, løsning is an en-word (common gender), which is why it is en løsning, not et løsning.

Because fælles is one of those adjectives that usually stays the same form.

You get:

• en fælles løsning
• et fælles mål
• fælles løsninger

So unlike many Danish adjectives, fælles does not usually add extra endings in these common uses.

Here selv om means even though or although.

You will also often see selvom written as one word. Learners should recognize both. In many modern texts, the one-word form is very common when it functions as a conjunction.

So in this sentence:

• selv om vi først var uenige = even though we were initially in disagreement

Because selv om introduces a subordinate clause, and subordinate clauses do not follow the normal Danish main-clause verb-second pattern.

Main clause:

• Vi var først uenige = We were at first in disagreement

Subordinate clause:

• ... selv om vi først var uenige

So after selv om, the subject vi comes before the finite verb var, and the adverb først can appear before the verb.

Here først means at first or initially.

It does not mean firstly in a list.

So the idea is:

• at the beginning, they disagreed
• later, they found a common solution

That contrast is important to the sentence.

Because the subject is vi = we, which is plural.

With predicate adjectives after være, Danish normally uses:

• singular: uenig
• plural: uenige

Examples:

• Jeg var uenig = I was in disagreement
• Vi var uenige = We were in disagreement

So uenige agrees with the plural subject vi.

Yes, a little.

Compare:

• Vi fandt en fælles løsning = We found a common solution
• Det lykkedes os at finde en fælles løsning = We managed to find a common solution

The second version adds the idea that it was not easy or that there was some challenge involved. It highlights the success of the effort, not just the result.

Yes.

Both are natural, but they differ in tense:

• Det lykkedes os at finde... = We managed to find...
• Det er lykkedes os at finde... = We have managed to find...

The first is a simple past statement. The second connects the result more clearly to the present.

Because selv om vi først var uenige is a subordinate clause.

In Danish, commas are often used before subordinate clauses like this. Depending on the comma system or style being followed, you may also see the sentence written without that comma. But the version with the comma is completely normal and easy for learners to understand.

A very literal version would be:

• It succeeded for us to find a common solution, even though we were at first in disagreement.

That is not natural English, but it helps show how the Danish grammar works.

A more natural English rendering is:

• We managed to find a common solution, even though we initially disagreed.