Singlet fission in covalently bound acene dimers in solution is driven by the interplay of excitonic and singlet correlated triplet 1(TT) states with intermediate charge-transfer states, a process which depends sensitively on the solvent environment. We use high-level electronic structure methods to explore this singlet fission process in a linked tetracene dimer, with emphasis on the symmetry-breaking mechanism for the charge-transfer (CT) states induced by low-frequency antisymmetric vibrations and polar/polarizable solvents. A combination of the second-order algebraic diagrammatic construction (ADC(2)) and density functional theory/multireference configuration interaction (DFT/MRCI) methods are employed, along with a state-specific conductor-like screening model (COSMO) solvation model in the former case. This work quantifies, for the first time, an earlier mechanistic proposal [Alvertis et al., J. Am. Chem. Soc. 2019, 141, 17558] according to which solvent-induced symmetry breaking leads to a high-energy CT state which interacts with the correlated triplet state, resulting in singlet fission. An approximate assessment of the nonadiabatic interactions between the different electronic states underscores that the CT states are essential in facilitating the transition from the bright excitonic state to the 1(TT) state leading to singlet fission. We show that several types of symmetry-breaking inter- and intra-fragment vibrations play a crucial role in a concerted mechanism with the solvent environment and with the symmetric inter-fragment torsion, which tunes the admixture of excitonic and CT states. This offers a new perspective on how solvent-induced symmetry-breaking CT can be understood and how it cooperates with intramolecular mechanisms in singlet fission.