The inclusion of nanoparticles has the potential to enhance the thermal efficiency of the base fluid. The field of nanofluid dynamics has attracted significant attention due to its wide range of practical applications such as fuel cells, solar energy, medication administration, heat transfer, microfabrication, coolant applications, and other related domains. The aim of this study is to examine the impact of Lorentz force, thermal radiation, joule heating, heat source and injection parameters, and Brownian and thermoporetic diffusions on the hybrid nanofluid over the moving wedge. The stability analysis is reported for the current study in order to confirm the stable solutions that make the study unique. Novelty of the current study is to investigate the hybrid nanofluid flow and its stability. The nanoparticles MoS2 and Ag are suspended in ethylene glycol and water used as host fluids. The numerical solution is obtained from the dimensionless first-order differential equations, which are obtained from the basic flow equations through similarity transformation variables. The influence of emerging factors on flow phenomena is reported via graphs. The positive eigenvalues report stable solutions, while the negative eigenvalues designate unstable solutions. It is perceived that due to Lorentz force, the velocity of the fluid declines while the temperature inside the fluid enhances. The velocity profile decreases while the temperature and concentration increase with increasing quantities of permeable factors. Similarly, the Forchheimer number causes to enhance the velocity and decrease the temperature and concentration profiles. The current analysis is validated by the published work.