This is an experimental study of psychological mechanisms of solving the so-called regular — that is, well-defined, closed, and noninsight problems in algebra. The results show that the balanced grouping of operations (in terms of Jean Piaget), which is necessary for solving linear equations, cannot provide the needed mechanism of the regular problems solving. In the absence of this structure, this kind of problems cannot be successfully resolved. On the other hand, its presence does not yet guarantee success. This kind of grouping (as all similar psychological structures) is therefore a necessary but not sufficient condition of successful regular problems solving.