Collaborative caching and processing at the network edges through mobile edge computing (MEC) helps to improve the quality of experience (QoE) of mobile clients and alleviate significant traffic on backhaul network. Due to the challenges posed by current grid powered MEC systems, the integration of time-varying renewable energy into the MEC known as green MEC (GMEC) is a viable emerging solution. In this paper, we investigate the enabling of GMEC on joint optimization of QoE of the mobile clients and backhaul traffic in particularly dynamic adaptive video streaming over HTTP (DASH) scenarios. Due to intractability, we design a greedy-based algorithm with self-tuning parameterization mechanism to solve the formulated problem. Simulation results reveal that GMEC-enabled DASH system indeed helps not only to decrease grid power consumption but also significantly reduce backhaul traffic and improve average video bitrate of the clients. We also find out a threshold on the capacity of energy storage of edge servers after which the average video bitrate and backhaul traffic reaches a stable point. Our results can be used as some guidelines for mobile network operators (MNOs) to judge the effectiveness of GMEC for adaptive video streaming in next generation of mobile networks.