Hexagonal patterns in Bénard-Marangoni BM convection are studied within the framework of amplitude
equations. Near threshold they can be described with Ginzburg-Landau equations that include spatial quadratic
terms. The planform selection problem between hexagons and rolls is investigated by explicitly calculating the
coefficients of the Ginzburg-Landau equations in terms of the parameters of the fluid. The results are compared
with previous studies and with recent experiments. In particular, steady hexagons that arise near onset can
become unstable as a result of long-wave instabilities. Within weakly nonlinear theory, a two-dimensional
phase equation for long-wave perturbations is derived. This equation allows us to find stability regions for
hexagon patterns in BM convection.