NOVELTY - Preparing a biodiesel product, comprises: preparing a heterogeneous catalyst system; placing an unrefined oil feedstock and an alcohol in contact with the system to form a reaction mixture including triglycerides, alcohol, free fatty acids (greater than 0.5 wt.%) and water (greater than 1 wt.%); heating the reaction mixture at 170-220 degrees C; allowing the transesterification of the triglycerides and the esterification of the fatty free acids to simultaneously occur for a predetermined amount of time to form fatty acid methyl esters resulting in the biodiesel product; and separating the catalyst.    USE - The method is useful for preparing the biodiesel product.    ADVANTAGE - The method provides biodiesel at low cost. The heterogeneous catalyst system has a high tolerance to the presence of water and free fatty acids (FFA) in the oil feedstock. The combination of zinc oxide and lanthanum oxides has higher catalytic activity. The presence of excess alcohol favors the occurrence of each reaction, thus maximizing the yield of fatty acid methyl esters. The addition of FAA accelerates reaction rate and shortens the time to achieve a high yield of fatty acid methyl esters. The catalyst system simultaneously catalyzes both the esterification of FAA and the transesterification of triglycerides present in the oil feedstock.    DETAILED DESCRIPTION - Preparing the biodiesel product from unrefined or waste oils, comprises: preparing a heterogeneous catalyst system, comprising a mixture of zinc and lanthanum oxides; placing an unrefined oil feedstock and an alcohol in contact with the catalyst system to form a reaction mixture, including triglycerides, alcohol, free fatty acids (greater than 0.5 wt.%), and water (greater than 1 wt.%); heating the reaction mixture at 170-220 degrees C; allowing the transesterification of the triglycerides and the esterification of the fatty free acids to simultaneously occur for a predetermined amount of time to form fatty acid methyl esters resulting in the biodiesel product; and separating the catalyst from the biodiesel product in order to collect the biodiesel product. INDEPENDENT CLAIMS are included for:    (1) a heterogeneous catalyst system, comprising zinc oxide having a mean grain size of 9.8-27.6 nanometers, and a mixture of lanthanum oxides, where the combination of zinc and lanthanum oxides has a zinc:lanthanum (Zn:La) bulk molar ratio of 1.2:1:0- 8.9:1, a surface area of 14.9-16.8 m2/g, a surface composition comprising zinc ion (Zn2+) (4.2-26.8%), lanthanum ion (La3+) (2.1-2.9%), and lattice oxygen (Olat) (23.2-32.9%), a surface atom ratio for Zn2+:La3+ is 1.4:1-11.6:1, and a surface atom ratio for (Zn2+ + La3+):Olat is 0.2:1-1.1:1; and    (2) the biodiesel product formed by reacting unrefined oil with an alcohol in the presence of the catalyst.