We present a 3D quantum wavepacket method for calculating state-to-state reactive cross sections for the A+BC-->AC+B reaction. The method avoids the coordinate problem (of A+BC arrangements being difficult to represent by AC+B coordinates, and vice versa) by solving the reactant-product decoupling (RPD) equations [T. Peng and J. Z. H. Zhang, J. Chem. Phys. 105, 6072 (1996)] in their further partitioned form [S. C. Althorpe, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 107, 7816 (1997)]. These equations decouple the nuclear dynamics Schrodinger equation into separate reactant, strong-interaction, and product regions, permitting different coordinates to be used in each region. We solve the equations using A+BC Jacobi coordinates in the reactant region, and AC+B Jacobi coordinates in the strong-interaction and product regions. In test calculations on the J = 0 H+H-2 reaction, we show that this partitioning of coordinate systems is much more efficient than using A+BC coordinates in the strong-interaction region (as was done in all previous applications of the RPD equations). We apply the method to the H+H-2 reaction (for J=0-24), and obtain the first state-to-state differential cross sections to be calculated by an exact quantum wavepacket method. The method will allow state-to-state cross sections to be calculated for the same reactions for which wavepacket methods can currently calculate total cross sections. (C) 2001 American Institute of Physics.