Dic: come out in the wash

come out in the wash (informal): to become known or apparent in the course of time.

it will all come out in the wash. (spoken):

1. used to tell someone not to worry about a problem because it will be solved in the future
2. used to say that the truth about something will be known in the end

come out in the wash (Slang)

1. To be revealed eventually: The real reasons for her resignation will come out in the wash.
2. To turn out well in the end: Don't worry: this project will come out in the wash.

something will come out in the wash. (INFORMAL)

1. used for saying that people will always find out the truth about something.
2. used for saying that you are sure you will find a solution to the problem you have.

... COLLINS, LDOCE, The American Heritage, MacMillan 

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come out in the wash: Fig. to work out all right. (Alludes to a clothing stain that can be removed by washing.) ex) Don't worry about that problem. It'll all come out in the wash.

It'll all come out in the wash. Fig. It does not matter.; No lasting damage has been done. 

• Tom: I feel so bad about what I said to Bill. I don't think he'll ever forgive me.
  Mary: Oh, don't worry. It'll all come out in the wash. 
• Jane: I'll never forgive myself for losing Mary's book.
  Charlie: Just tell her you're sorry, and offer to pay for the book. It'll all come out in the wash.

... McGraw-Hill Dictionary of American Idioms and Phrasal Verbs

come out in the wash : (informal) if something secret or unpleasant comes out in the wash, people discover the truth about it. 

• They don't want the police to investigate, because they're afraid of what might come out in the wash.

It'll all come out in the wash.  (informal) something that you say in order to tell someone not to worry because mistakes or problems will not have a serious or permanent effect. 

• It was the wrong thing to say, but don't get too upset, I'm sure it'll all come out in the wash eventually.

.... Cambridge Idioms Dictionary