A novel adsorbent, Fe‐Mn‐Zr metal oxide nanocomposite was synthesized and investigated for removal of methyl orange (MO) and eosin yellow (EY) dyes from binary dye solution. The magnetic nanocomposite has shown surface area of 143.01 m2/g and saturation magnetization of 15.29 emu/g. Optimization was carried out via response surface methodology (RSM) for optimizing process variables, and optimum dye removal of 99.26% and 99.55% were obtained for MO and EY dye, respectively with contact time 62 min, adsorbent dose 0.45 g/l, initial MO concentration 11.0 mg/l, and initial EY concentration 25.0 mg/l. A feed forward back propagation neural network model has shown better prediction ability than RSM model for predicting MO and EY dye removal (%). Adsorption process strictly follows Langmuir isotherm model, and enhanced adsorption capacities of 196.07 and 175.43 mg/g were observed for MO and EY dye, respectively due to synergistic effects of physicochemical properties of trimetal oxides. Surface adsorption and pore diffusions are the mechanisms involved in the adsorption as revealed from kinetic studies.