Macbook Pro 2010 Screen goes blank
I would suggest visiting a Apple Authorized Service Provider to troubleshoot this (what i suspect is a hardware issue)
https://www.apple.com/support/macbookpro-videoissues/

Unfortunately MacBook Pro (15-inch, Mid 2010) intermittent black screen or loss of video Quality Program has ended
https://support.apple.com/en-us/HT203554