m取值范围为m<=-1
设f(x)=x^2-4mx+2m+6,若A∩B=空集,则f(x)图像对称轴x=2m>0且f(0)>=0,综合解得m>0,所以要A∩B≠空集,首先要m<=0.又根据方程有解,得16m^2-4(2m+6)>=0,解得m<=-1或m>=3/2.综合之前m<=0,得到结果为m<=-1.