CORP ACFT PENETRATED ADJACENT ATC FAC AIRSPACE WITHOUT COORD OR HANDOFF. OPERATIONAL DEVIATION.

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I WAS WORKING DEP RADAR W AND DEP RADAR E COMBINED. WE WERE IFR DUE TO REDUCED VIS. SINCE I HAD RPTED TO WORK 40 MINS EARLIER; NO ONE HAD SUCCESSFULLY MADE AN APCH TO A FULL STOP LNDG. THEREFORE; WE HAD SEVERAL ACFT HOLDING IN OUR AIRSPACE DECIDING ON WHAT THEY WERE GOING TO DO. I DID HAVE AN ASSOCIATE HELPING ME TO PUT NEW FLT PLANS IN AND ANSWER LANDLINES. AT THE TIME OF THE DEVIATION; I WAS WORKING 8 AIRPLANES; MOSTLY ON THE W SIDE; AND WATCHING 2 POINTOUTS. THERE WAS 1 AIRPLANE ENRTE TO RDU; CORP X; THAT I DID NOT HDOF TO GSO APCH BEFORE HE XED THE BOUNDARY. HE WAS THE ONLY PLANE ON THE E SIDE AND BECAUSE OF ALL THE DISTR ON THE W SIDE; I FORGOT ABOUT HIM. GOS APCH COULD HAVE CARED LESS; AND THEIR COMMENT WAS THAT WE OWED THEM ONE. ONE DEFINITE CAUSAL FACTOR WAS HAVING TO WORK DEP RADAR W AND DEP RADAR E COMBINED. THAT ENTAILS WATCHING APPROX 90 MI RADIUS. THIS IS ALSO A PROC THAT WE HARDLY EVER DO. NORMALLY WE COMBINE THE ARR RADAR W TO THE DEP AND THE ARR RADAR E TO THE DEP E. IF THE SCOPES HAD BEEN COMBINED THE WAY WE NORMALLY DO IT; THIS PROBABLY NEVER WOULD HAVE HAPPENED.