<p>Factor structural imbalances brought about by factor market incompleteness can lead to a significant divergence in the marginal returns of factor inputs between high and low-efficiency firms, which emphasizes the necessity of a rational allocation of factors. The study proposed a meta-heuristic optimization random forest model with strong interpretability to identify the nonlinear partial dependencies, balance points, and balance intervals of key factors for low-carbon development in manufacturing and to reveal the balance and synergy effects of factor allocation. The findings reveal that: (1) There are significant differences in the key factors under different regions and industries. (2) The nonlinear partial dependence relationship curve of manufacturing low-carbon development on key factors shows four shapes: S-shaped, anti-S-shaped, U-shaped, and inverted U-shaped. (3) Controlling key factor inputs to lie in the balance interval of the partial dependence curve and applying threshold control under the intensive margin can effectively achieve the marginal benefit maximization. (4) The low-carbon development potential can be further exploited by fully utilizing the synergistic and complementary relationship between the combination of technology and data factors. Meanwhile, it is necessary to strengthen clean energy substitution and promote industrial upgrading to avoid the offsetting of the original synergistic gains by high-carbon energy consumption and industrial scale expansion. The study has constructed an expandable mechanism exploration methodology system, and the mining of factor role laws can provide theoretical supplementation and practical guidance for the formulation of targeted low-carbon development paths for manufacturing industries in sub-regions and sub-industries.</p> Graphical Abstract <p></p>