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.]
(..) I don't have change. You have till the afternoon. There is someone else I can hire if you can't come. OK. Termeh! Your laundry! You're not coming? - Why are you taking your books? - I want them. All this for just weeks? - Thank you. (..)2011 A Separation
(..) There is some housework too, but the main work is giving him his medication on time, keeping him away from the stove, from leaving the house. Termeh, get your laundry. You have to be here at so I can go to work. is too early. I'll have to leave my house at to get here by then. (..)2011 A Separation