Quantified constraint satisfaction problem (QCSP) is a central problem in artificial intelligence and automated reasoning. The tractable class is an important method to analyze its computation complexity. This study proposed a new method to determine tractability of quantified variables by analyzing constraint structures and the ordering of universally quantified variables in the prefix on a binary QCSP. Based on this method, the existing tractable class was extended with the broken-triangle property, and then a more generalized hybrid tractable class was proposed. Furthermore, an application was presented that was identifying backdoor sets through the new tractable class, and the experimental results were analyzed to show the size of backdoor sets identified by those hybrid tractable classes. To perform the experiment, a state-of-the-art QCSP solver was modified based on a backtracking algorithm by integrating a backdoor set detection module, and the advantage of the new generalized tractable class is shown where the size of backdoor set identified by it is smaller than the existing one on randomly generated instances. Finally, it is indicated that the method proposed in this study can be employed to extend other hybrid tractable classes.