Does the multiverse explain away the fine-tuning of the universe?

No - and here is why it doesn't dissolve the mystery. The fine-tuning data itself is not really in dispute: the constants of physics fall within strikingly narrow life-permitting ranges, a point conceded even by atheist physicists like Roger Penrose. The multiverse is a genuine rival explanation, not a scientific disproof of design: if there are countless universes with randomly varying constants, then life-permitting ones are bound to arise somewhere, and of course we find ourselves in one - we could hardly find ourselves in a universe that forbids observers.

But two things keep it from being the refutation it is sometimes taken to be. First, the multiverse is a metaphysical rival to design, not a scientific disproof of it. The mechanisms proposed to generate a multiverse appear to require their own fine-tuning to work - so the problem is arguably relocated rather than removed. And such theories face further puzzles (like the "Boltzmann brain" problem) and have no agreed observational test. Second, and this is the honest point cutting the other way: the design inference itself faces a real technical difficulty, the "measure problem" - specifying a defensible probability over the space of possible universes is genuinely unfinished business, and its best proponents admit as much.

So the fair verdict is that fine-tuning leaves us with serious options - chance (typically via a multiverse), necessity, or design - and no side gets to declare victory. What no one should say is that "scientists agree the universe is designed": the data are widely conceded, but design is a contested philosophical inference. The multiverse does not dissolve the mystery; it is one more serious contender within it.