We consider the problem of finding solutions to systems of polynomial equations over a finite field. Lokshtanov et al. [SODA'17] recently obtained the first worst-case algorithms that beat exhaustive search for this problem. In particular for degree-d equations modulo two in n variables, they gave an O^{∗}2^{(1}−1/(5d))^{n} time algorithm, and for the special case d = 2 they gave an O^{∗}2^{0.876n} time algorithm. We modify their approach in a way that improves these running times to O^{∗}2^{(1}−1/(2^{7}d))^{n} and O^{∗}2^{0.804n}, respectively. In particular, our latter bound - that holds for all systems of quadratic equations modulo 2 - comes close to the O^{∗}2^{0.792n} expected time bound of an algorithm empirically found to hold for random equation systems in Bardet et al. [J. Complexity, 2013]. Our improvement involves three observations: 1. The Valiant-Vazirani lemma can be used to reduce the solution-finding problem to that of counting solutions modulo 2. 2. The monomials in the probabilistic polynomials used in this solution-counting modulo 2 have a special form that we exploit to obtain better bounds on their number than in Lokshtanov et al. [SODA'17]. 3. The problem of solution-counting modulo 2 can be “embedded” in a smaller instance of the original problem, which enables us to apply the algorithm as a subroutine to itself.