It would take a *lot* of work to get that thing to sound remotely listenable.
That flimsy sheet metal would rattle like hell at any sort of volume. What you could do it take the whole machine apart, and sound dampen the hell out of the back sides (the spray type would probably be best, I'm sure there are many tight corners). Then you would rant to internally brace that thing with wood as well. THEN, you would need to create a sealed chamber in there designed to the t/s parameters of the subs. Just dropping a speaker into a hole is a sure fire way to be dissappointed at the sound you get.
Sound pressure exerted by subs can be very powerful, putting a sub into something that was designed for another purpose can be difficult if it does not have structural integrity. I've seen guys put subs into old beer kegs, that works great because they are strong, a washing machine isn't.
Don't want to discourage you from the project, but you need to think about these factors.