This research investigates the stability of rotating-disk boundary-layer flow in a Carreau fluid, a widely used model for shear-thinning and thickening non-Newtonian fluids. Using mathematical modeling, numerical methods, and linear stability analysis, the study examines how fluid rheology influences flow stability and the onset of disturbances. The findings contribute to a better understanding of complex fluid behaviour and provide insights relevant to industrial and engineering applications involving non-Newtonian flows.