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Strong Coulomb interactions in single-layer transition metal dichalcogenides (TMDs) result in the emergence of strongly bound excitons, trions, and biexcitons. These excitonic complexes possess the valley degree of freedom, which can be exploited for quantum optoelectronics. However, in contrast to the good understanding of the exciton and trion properties, the binding energy of the biexciton remains elusive, with theoretical calculations and experimental studies reporting discrepant results. In this work, we resolve the conflict by employing low-temperature photoluminescence spectroscopy to identify the biexciton state in BN-encapsulated single-layer WSe. The biexciton state only exists in charge-neutral WSe, which is realized through the control of efficient electrostatic gating. In the lightly electron-doped WSe, one free electron binds to a biexciton and forms the trion-exciton complex. Improved understanding of the biexciton and trion-exciton complexes paves the way for exploiting the many-body physics in TMDs for novel optoelectronics applications.