It looks like one I have which is determined to establish itself in my garden! I don't mind it in places but it can be 'robust', it sends out runners which root so that might be the reason it appears to reseed a lot but it probably reseeds a lot too!
Look at Creeping Buttercup, Ranunculus repens, the leaves have faint light spots on them. The broader leaves in Sherry's photo I think are the buttercup, the thinner ones look like Geranium. The roots are white and quite strong, they like moist soils.
https://www.google.co.uk/searc...
http://www.lawnweeds.co.uk/cre...
