A new algorithm for computation of the simultaneous chemical and phase equilibrium in homogeneous as well as in heterogeneous liquid mixtures is presented. The algorithm is based on the concept of transformed coordinates and the rigorous tangent plane stability test, Using transformed coordinates, we restrict the solution space to the compositions that are already at chemical equilibrium. This reduces the dimension of the problem by the number of independent reactions and makes it possible to represent phase equilibrium in reactive systems in a similar way as in non-reactive mixtures. A global algorithm for stability analysis in multi-component, multiphase reactive mixtures has been developed. It is based on the Gibbs tangent plane stability test. In our approach, we locate all stationary points of the tangent plane distance function expressed in terms of transformed coordinates. The algorithm is independent of the specific fluid model, is self-starting and significantly improves the robustness and reliability of multiphase reactive equilibrium calculations. The method has been implemented and tested on a variety of problems, in which solutions for the entire phase diagram were found without fail, and difficult cases were successfully calculated. illustrative examples of Gibbs free energy surface and reactive phase diagrams: isothermal liquid-liquid and isobaric vapor-liquid-liquid equilibrium diagrams for multiple liquid phases are presented.