Solving dense linear systems of equations is a fundamental problem in scientific computing. Numerical simulations involving complex systems represented in terms of unknown variables and relations between them often lead to linear systems of equations that must be solved as fast as possible. We describe current efforts toward the development of these critical solvers in the area of dense linear algebra (DLA) for multicore with GPU accelerators. We describe how to code/develop solvers to effectively use the high computing power available in these new and emerging hybrid architectures. The approach taken is based on hybridization techniques in the context of Cholesky, LU, and QR factorizations. We use a high-level parallel programming model and leverage existing software infrastructure, e.g. optimized BLAS for CPU and GPU, and LAPACK for sequential CPU processing. Included also are architecture and algorithm-specific optimizations for standard solvers as well as mixed-precision iterative refinement solvers. The new algorithms, depending on the hardware configuration and routine parameters, can lead to orders of magnitude acceleration when compared to the same algorithms on standard multicore architectures that do not contain GPU accelerators. The newly developed DLA solvers are integrated and freely available through the MAGMA library.