a=-3/2
∵当a-2=-3时,a=-1,2a²+5a=2-5=-3
集合出现两个-3,所以a-2≠-3
∴2a²+5a=-3
2a²+5a+3=0
(2a+3)(a+1)=0
a=-3/2或a=-1(舍去)
∴a=-3/2