Don’t remove anything get a can of Weldwood brush on cement and brush it on the old adhesive brush it on the old carpet and secure the carpet

this carpet is a gray triangle that looks like indoor outdoor carpet

 

I would use some of this.

 

Thanks for the advice gentlemen.
Which of the above suggestions works best?
I've tried a mix of the usual solutions - paint remover, nail polish remover, brake cleaner, glue remover, WD40, PBlaster, etc - non really had an effective impact.
Should I expect to have to put some elbow grease into it?
I want to get the area perfectly free of lacquer

What effectively removes old glue but not paint to make the blue circled areas like the red circled area?

 

Ospho is great. have used it for 40 years in marine environment with boats and cars.