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When thrust equals drag, the airplane keeps moving at whatever speed it is already moving.

Thrust needs to exceed drag in order for the aircraft to accelerate forward.  According to Newton’s first law, an object in motion tends to stay in motion unless acted on by an outside force.  If lift equals weight and thrust equals drag, there is no net outside force acting on the aircraft. That means it will keep going at the same altitude and speed until one of the forces changes.