one hand washes the other (and both wash the face)

proverb All parties involved will benefit from helping each other and/or working together toward the same goal. Look, if you feature our company's logo during your campaign, we get a major boost in advertising visibility, and you get a bump in your campaign funding—one hand washes the other! The criminal organization has several politicians and most of the police force in its pocket, with everyone seeing a profit from illegal activities. One hand washes the other, and both are washing the face!

Mutually helping one another. A 1906 dictionary of Latin quotations lists manus manam lavat, ascribed to Seneca the Younger (5 b.c.–65 a.d.), and the current phrase may indeed be a translation derived from this source. In Deborah Eisenberg’s “A Cautionary Tale,” the term is used with regard to a character paying more to sublet an apartment than the original renter pays. “‘One hand washes the other,’ Marcia had remarked cheerfully when she explained this to Patty.” Another version of this cliché is “You scratch my back and I’ll scratch yours.” Novelist Lee Child had it in 61 Hours (2010): “He wanted combination radiation shelters and living accommodations built. He talked to the Air Force. He scratched their backs, they scratched his.” See also quid pro quo.