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Others have already pointed out that self-answering is not only allowed, but even encouraged when you've got some insight you think would be of value to others.

Over at the Electrical Engineering site we've even taken this a step further with the <i>Papers</i> category.  It can be a more appropriate way to present your new insight than artificially asking, then answering.  Some sites have similar mechanisms, like the <i>Recipes</i> category on Cooking.

On sites that have both kinds of posts, use Q&A if you're willing or want others to provide possibly different viewpoints or different ways of presenting the solution.  If you want to create a more careful presentation without clutter from others, write a Paper or similar.