The Boolean satisfiability problem (SAT) refers to whether there is a truth assignment that satisfies a given Boolean formula, which is the first confirmed NP complete problem that generally does not exist a polynomial time algorithm unless P=NP. However many practical applications of such problems often take place and are in need of an effective algorithm to reduce their time complexity. At present, many scholars have studied the problem of SAT with clause length not exceeding k (k-SAT). From global search to local search, a large number of effective algorithms, including random algorithm and determination algorithm are developed, and the best result, including probabilistic algorithm and deterministic algorithm for solving k-SAT problems, is that the time complexity is less than O((2-2/k)ⁿ), and when k=3 the time complexity of the best algorithm is O(1.308ⁿ). However, there is little literature about SAT problems that are more general than clause length k. This paper discusses a class of separable satisfiability problems (SSAT), in particular, the problem of 3-regular separable satisfiability (3-RSSAT) where the formula can be separated into several subformulas according to certain rules. The paper proves that 3-RSSAT problem is NP complete problem because any SAT problem can be polynomially reduced to it. To determine 3-regular separability of the general SAT problem, an algorithm is given with time complexity is no more than O(1.890ⁿ). Then by using the result in the matrix multiplication algorithm optimal research field, an O(1.890ⁿ) exact algorithm is constructed for solving the 3-RSSAT problem, which is the WELL algorithm independent of clause length.