I'm responding to Richtig123's comment about not being able to get his head around transitive and intransitive verbs, but this thread is too long so I can't reply directly.
Few links that may be useful: http://pages.ucsd.edu/~dkjordan/eo/colloq/colloq120.html#sec12-4
What is the difference between zorgi and maltrankvil(iĝ)i?
In this thread I answered the question "Why not 'Ni ne zorgu'?" with:
- Zorgi means to care -- like taking care of something. I say "fari al si zorgojn" when you're worrying about something.
There are some good answers in the following threads.
The root of the word is "trankvil" (like the English "tranquil", "calm"). the "iĝ" changes it to "become calm". The ending "u" makes it imperative, that is, telling someone to do something. So "trankviliĝu" is telling somebody to become calm. Putting "mal" at the beginning makes at mean the opposite, so "maltrankviliĝu" is telling somebody to become "uncalm", or as we would say, upset, worried.
This is called the jussive mood, and in Esperanto the imperative -u is supplied to jussive verbs.