Solving nonlinear equation systems is a significant and challenging task in the field of numerical computation, aiming to identify multiple roots in a single run. To fully utilize the optimization information in the neighborhood-based crowding differential evolution algorithm while maintaining good population diversity and computational resource efficiency, a nearest-neighbor frequency information-guided multi-mutation differential evolution algorithm is proposed. The multi-mutation strategy groups individuals based on their fitness values, and each group uses different mutation operators to achieve comprehensive learning of global and individual neighborhood information, thereby enhancing the algorithm""s ability of multi-root joint solution. The frequency information guidance mechanism of neighboring individuals utilizes the frequency of an individual being selected as a neighboring individual to improve the efficiency of the evolutionary process and enhance the exploration ability of potential roots. Experimental results show that the proposed algorithm has higher computational resource utilization efficiency, higher root-finding rate and success rate compared to other comparison algorithms.