Let V be full volume.
We are told: V/2 -420 = V/8
Subtract V/8 from both sides: V/2 - V/8 - 420 = 0
Add 420 to both sides: V/2 - V/8 = 420
Simplify the left hand side: 3V/8 = 420
Multiply both sides by 8/3: V = 420*8/3
Simplify: V = 140*8 or V = 1120 gallons