Mg-Fe substitution is most commonly seen in natural solid solution minerals. High resolution X-ray spectroscopy has recently demonstrated that the major lower mantle (LM) minerals undergo a high-to-low spin transition at LM pressures (23-135 GPa). Previous failures of standard DFT and "LDA+U" approaches to describe this phenomenon have hindered its investigation and consequences of fundamental importance to geophysics, such as heat transport in Earth's mantle. Here, using the latest rotationally invariant first principles formulation of LDA+U with optimized effective U, we report the first successful study of this transition in low solute concentration (Mg(1-x)Fex)O, magnesiumwustite. This is believed to be the second most abundant phase of Earth's LM. This encouraging result appears to open for exploration a new class of problems of enormous significance to deep Earth geophysics