
schließlich
finally
At the end of a process or development, or after a long wait; at last.
Nach stundenlanger Diskussion haben wir uns schließlich auf einen Kompromiss geeinigt.
After hours of discussion, we finally agreed on a compromise.
finally / after all
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finally
At the end of a process or development, or after a long wait; at last.
Nach stundenlanger Diskussion haben wir uns schließlich auf einen Kompromiss geeinigt.
After hours of discussion, we finally agreed on a compromise.

after all
Introduces a justification or an important objection; means roughly 'immerhin' (after all) or 'man darf nicht vergessen, dass' (one must not forget that).
Sei nicht so streng mit ihm, er ist schließlich noch ein Kind.
Don't be so strict with him; he is still a child, after all.
The word 'schließlich' is derived from 'der Schluss' (the end). This connection to the idea of closure helps you understand the main meaning 'am Ende' (in the end) or 'endlich' (finally).
Wir haben lange diskutiert und schließlich eine Lösung gefunden.
We discussed it for a long time and finally found a solution.
'Schließlich' can be meant temporally ('endlich' = finally) or as a justification ('immerhin' = after all). The temporal meaning concludes a process, while the justifying meaning provides an important reason or context.
Zuerst hat es geregnet, dann geschneit, und schließlich kam die Sonne raus.
First it rained, then it snowed, and finally the sun came out.
When 'schließlich' is at the beginning of a main clause in position 1, the verb follows directly in position 2. This word order is called inversion.
Schließlich verstand er das Problem und konnte es lösen.
Finally, he understood the problem and was able to solve it.
finally / finite
Both words can express that something happens at the end of a longer process. „Endlich“ usually emphasizes relief or impatience after waiting. „Schließlich“ is more neutral and indicates the endpoint of a process or a final conclusion. Use „endlich“ when there is a strong sense of anticipation and „schließlich“ for a matter-of-fact sequence of events.

Nach mehreren Versuchen gelang der Start schließlich.
After several attempts, the launch eventually succeeded.
Nach drei Stunden Wartezeit kam der Bus endlich.
After waiting for three hours, the bus finally arrived.