A useful procedure for finding all the roots of the type of equation indicated in the title, typically used in vapor-liquid separations, is presented. The proposed procedure is the result of a matrix-based analysis to generate a Standard Eigenvalue Problem. The eigenvalues of the resulting matrix system are exactly the roots of the equation indicated in the title. Numerical experiments are presented to show the goodness of the proposed procedure. 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.