Solving equations and system of equations is a crucial feature of Computer Algebra Systems and Polynomial factorization is one of the fundamental tools to implement solvers. Currently, SymEngine has an implementation of Univariate Polynomials, MultiVariate Polynomials, Sets and Finite Fields.
SymPy has a robust solvers module. I would like to port basic solvers like univariate solvers, trigonometric solvers and System of linear Equations to SymEngine. SymEngine's Set module is not matured enough, So I will also improve Sets to facilitate Solvers. In SymPy, Currently Major work is going around replacing solve with solveset. So, rather that porting solve, I would port solveset to SymEngine. After implementing basic solvers module, I would also implement some applications of solvers like eigenvectors and eigenvalues of a matrix.