sich entspannen
to relax
To recover, calm down, and reduce physical or mental tension.
Nach einem langen Arbeitstag entspanne ich mich gerne mit einem guten Buch.
After a long day at work, I like to relax with a good book.

to relax
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to relax
To recover, calm down, and reduce physical or mental tension.
Nach einem langen Arbeitstag entspanne ich mich gerne mit einem guten Buch.
After a long day at work, I like to relax with a good book.

The verb consists of the prefix 'ent-' and the stem 'spannen' (to tense/stretch). The prefix 'ent-' often means the opposite or the removal of something. Since 'spannen' means 'anspannen' (to tense), 'entspannen' literally means 'to take away tension'.
Eine Massage kann helfen, verspannte Muskeln zu entspannen.
A massage can help relax tense muscles.
Pay attention to the difference: 'sich entspannen' (to relax) is reflexive and means that a person calms down. 'Etwas entspannen' (to ease/relax something) is transitive and means that you loosen a thing or ease a situation.
Ich entspanne mich am Abend gerne auf dem Sofa.
I like to relax on the sofa in the evening.
When someone relaxes, the way they do it is often stated with the prepositions 'bei' (while/during) or 'mit' (with). Typical phrases are 'sich bei einem Spaziergang entspannen' (to relax during a walk) or 'sich mit Musik entspannen' (to relax with music).
Am Wochenende entspanne ich mich am liebsten bei der Gartenarbeit.
On the weekend, I most like to relax by gardening.
When 'entspannen' (to ease/relax) has an object, that object can be literal, such as 'die Muskeln' (the muscles) or 'die Hand' (the hand). But it can also be used figuratively, for example 'die Lage' (the situation), 'die Atmosphäre' (the atmosphere), or 'die Beziehungen' (the relations).
Der Mediator versuchte, die angespannte Lage zwischen den Parteien zu entspannen.
The mediator tried to ease the tense situation between the parties.
to solve / loosen
'lösen' and 'entspannen' can both have to do with loosening. Use 'lösen' when something is tight or fixed and is opened, loosened, or separated, for example a knot or a fastening. Use 'entspannen' when tension decreases: in muscles, in the body, in thoughts, or also in a tense situation. The words can be confused because both make something less tight or less tense. For knots and fixed connections, 'lösen' fits. For rest, calm, and less stress, 'entspannen' fits.

Nach der Arbeit entspannt sich die Fahrerin zu Hause bei leiser Musik.
After work, the driver relaxes at home with quiet music.
Nach dem Unterricht löst sie vorsichtig das Band um die Mappe.
After class, she carefully unties the ribbon around the folder.