die Regelung
regulation
A binding rule, provision, or agreement that organizes a particular matter or process.
Es gibt eine neue gesetzliche Regelung für die Arbeitszeiten.
There is a new legal regulation for working hours.

regulation / control
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regulation
A binding rule, provision, or agreement that organizes a particular matter or process.
Es gibt eine neue gesetzliche Regelung für die Arbeitszeiten.
There is a new legal regulation for working hours.

'Regelung' (regulation/control) is derived from the verb 'regeln' (to regulate/arrange). The ending '-ung' turns a verb into a feminine noun ('die Regelung') that describes the process or result of the action.
Wir müssen das Problem schnell regeln.
We need to sort out the problem quickly.
In the sense of a rule or provision, 'Regelung' (regulation) is often used in official contexts. Typical combinations are 'eine gesetzliche Regelung' (a legal regulation), 'eine Regelung treffen' (to make an arrangement), or 'eine klare Regelung finden' (to find a clear arrangement).
Die Partner haben eine faire Regelung für die Aufteilung der Kosten getroffen.
The partners made a fair arrangement for dividing the costs.
When it is about adjusting devices, you can recognize this meaning from the technical vocabulary. Common combinations are 'die Regelung der Temperatur' (temperature control), 'die Regelung der Geschwindigkeit' (speed control), or 'die elektronische Regelung' (electronic control).
Die stufenlose Regelung der Lautstärke ist sehr praktisch.
The stepless adjustment of the volume is very practical.
solution
'die Lösung' and 'die Regelung' can both help organize or end a problem. 'Lösung' generally means a way in which a problem disappears or gets better. 'Regelung' more often means a fixed rule, agreement, or technical setting that controls something. The words are easy to confuse because a regulation can be a solution. But not every solution is a regulation. If it is about an idea or method, 'Lösung' fits. If it is about clear rules, responsibilities, or settings, 'Regelung' fits better.

Im Büro gibt es jetzt eine neue Regelung für das Arbeiten von zu Hause.
There is now a new policy in the office for working from home.
Für den Streit im Team suchen wir eine faire Lösung.
We are looking for a fair solution to the conflict in the team.