both / neither

[mehmetcalimli]

Is it possible to say "Both of them aren't worried" instead of
"Neither of them is worried"?

[VenusEnvy]

Is it possible to say "Both of them aren't worried" instead of "Neither of them is worried"?

No, I'm sorry, Meh.

I don't think that you can negate both in this way. I'll wait for an expert to confirm this...
"Both of them are worried." (correct)
"Both of them aren't worried." (incorrect)

Your second sentence is correct. Neither means not one, nor the other.

[Tdol]

If you look at Google results for the phrase, you'll see t does exist, but is very rarely used indeed:
http://www.google.com/search?hl=en&l...22&btnG=Search