Let's not 'air our dirty laundry' [=discuss our problems, make our problems known] in public.
The company is trying to keep its 'dirty laundry' from being aired/washed in public.
I have to 'do the laundry' today. [=to wash the dirty clothes, towels, etc.]
(..) Fucking babies. - Hey, Mom. - Hello, dear. I washed your sheets. - What's that? - Arthur's handkerchief. - You're doing his laundry? - It must have gotten mixed into my things. - That's gross. - It's just a hanky. I know, and hankies are gross. - First of all, the word is gross. Hanky. (..)2003 TvShow: Six Feet Under Title: Making Love Work Season: 3 Episode 6