I am not sure about the Detergent - which has borax mixed with soaps and probably other water conditioners to be use alone for laundry.
Borax Powder is a laundry additive - used in addition to your choice of laundry soap.
As a dry powder it kills insects by clogging the pores in the their exoskeleton that are part of their respiratory system.
A few years ago I had an invasion of German roaches (came with a used cage that came with a glider, apparently living INSIDE the metal frame where washing the cage did not get to them.)
I finally got rid of them by using borax powder sprinkled under the paper liners in my cages because that is where they hide during the day. I put the powder in the holes of the cage frame as well to get rid of the ones that hid inside. I also put it under the baseboards in the glider room and in the sliding door track that separates the glider room from the living room.
It does work well for fleas in carpets too.