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The liquid metal-liquid silicate partitioning of molybdenum and tungsten during core formation must be well-constrained in order to understand the evolution of Earth and other planetary bodies, in particular because the Hf-W isotopic system is used to date early planetary evolution. We combine 48 new high pressure and temperature experimental results with a comprehensive database of previous experiments to re-examine the systematics of Mo and W partitioning. W partitioning is particularly sensitive to silicate and metallic melt compositions and becomes more siderophile with increasing temperature. We show that W has a 6+ oxidation state in silicate melts over the full experimental fO2 range of $Δ$IW -1.5 to -3.5. Mo has a 4+ oxidation state and its partitioning is less sensitive to silicate melt composition, but also depends on metallic melt composition. DMo stays approximately constant with increasing depth in Earth. Both W and Mo become more siderophile with increasing C content of the metal, so we fit epsilon interaction parameters. W and Mo along with C are incorporated into a combined N-body accretion and core-mantle differentiation model. We show that W and Mo require the early accreting Earth to be sulfur-depleted and carbon-enriched so that W and Mo are efficiently partitioned into Earth's core and do not accumulate in the mantle. If this is the case, the produced Earth-like planets possess mantle compositions matching the BSE for all simulated elements. However, there are two distinct groups of estimates of the bulk mantle's C abundance in the literature: low (100 ppm), and high (800 ppm), and all models are consistent with the higher estimated carbon abundance. The low BSE C abundance would be achievable when the effects of the segregation of dispersed metal droplets produced in deep magma oceans by the disproportionation of Fe2+ to Fe3+ plus metallic Fe is considered.