Over the last 4 years I've been trying to get rid of this weed. i will not use chemicals because it's in my garden. This weed sends out roots to spread throughout my garden. This is a rel plague. I need help!!!

Actually, it's a herb! But too much of a good thing, etc.

http://www.ces.ncsu.edu/hil/hil-8101.html

Natural controls include black plastic, mulch, etc.

Hope this is useful
John/Ecologicalsgardens

Depending on how close to other plants the weeds are, you could disrupt the photosynthesis constantly by burning with a torch, fatty acids, vinegar sprays (requires soil remediation if over applied), more expensive options such as steam or infra red weeding equipment will do the trick. A great option would be to hire some local kids to pull the weeds for you.