This research presents a comprehensive modeling approach for the flight dynamics of a hybrid compound helicopter, employing classical mechanics methods. The derived non-linear mathematical model encompasses the individual components of the aircraft, including the rotor, propellers, wings, fuselage, and empennage, which are then integrated into a unified dynamics framework through the final Equations of Motion. Notably, the model incorporates a conventional first-order steady flapping motion and quasi-dynamic inflow modeling for both the rotor and propellers. The resulting model represents a complete 9 Degree-of-Freedom system, augmented with 6 mechanical ones and an additional 3 for the inflows of the rotor and the two propellers. As an over-actuated coupled system, it offers 7 available controls; rotor collective pitch, rotor longitudinal and lateral cyclic pitch, port-side and starboard-side propeller pitch, elevator deflection, and rudder deflection. The primary objective of this study is to identify operating trim points during forward flight, ranging from hover to the observed maximum airspeed of 255 knots. Achieving trim through numerical optimization involves a control allocation process utilizing a mapping function that prioritizes the auxiliary propulsion. The research findings demonstrate the successful implementation of a slowed-rotor strategy at high speeds, effectively mitigating compressibility effects, and a linearized mathematical system is derived, providing essential insights for future stability analysis and control system design. These outcomes contribute valuable information toward the advancement of hybrid compound helicopter technology.