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Well... "промывка" is more energetic and a little bit more colloquial than "промывание". Small difference in style only.

Brainwashing - промывка мозгов
Brainwashed one - человек с промытыми мозгами

It means exactly the same but there is no way to say it in one word.

There is word "распропагандированный" (try to...