A systematic numerical investigation is carried out to understand magnetohydrodynamic stability of the ideal infernal-kink instability in tokamak plasmas with both negative triangularity (neg-D) shaping and negative central shear for the equilibrium safety factor profile. The latter is motivated by the desire to form the internal transport barrier in the neg-D configuration, which is known to have difficulty in forming the edge transport barrier. The infernal-kink mode is generally found to be more unstable in neg-D plasmas as compared to their positive D-shaped (pos-D) counterpart. This is mainly due to less favorable (or even unfavorable) average magnetic curvature near the radial location of the minimum safety factor () as compared to the pos-D configuration. The larger Shafranov shift associated with the neg-D shape helps the mode stabilization but is not sufficient to overcome the destabilizing effect due to bad curvature. Strong poloidal mode coupling due to plasma shaping (toroidicity, elongation, triangularity, etc.) helps explain the slight shift with respect to that predicted by the analytic theory of the peak location of the computed mode growth versus .