A unified equation-solving framework for the direct determination of limits of feasibility and/or conditions of feasibility/infeasibility is presented. This approach is based on an implicit formulation due to Griewank and Reddien (1984) and is extended to the complex domain to both ensure finite step termination in cases where no limits of feasibility are present in the real domain and to find and verify conditions of infeasibility. It is shown that limits of feasibility can be determined by adding a minimal set of implicit equations that define singularity to the process model, which are readily available through the factorization of any rank deficient Jacobian matrix, such that the resulting appended system of model equations is nonsingular. Conditions of feasibility/infeasibility, on the other hand, can be identified by the calculation of singular points that correspond to nonzero stationary points in the two-norm of the model functions, curvature and the nature of neighboring solutions. A simple chemical process example is presented to provide geometric insight and to illustrate the salient features of the method.