A diversity-oriented, multicomponent convergent synthesis of symmetrical triazines through a one-pot protocol is presented in this research project. The assembly of trisubstituted triazines was initially carried out using easily available reagents through three different protocols, i.e., conventional, MW-assisted synthesis, and solid-supported MW-assisted synthesis using organic and inorganic support to carry out a comparative analysis as to which procedure best corresponds to a greener synthesis protocol. The compounds formed were characterized for structure elucidation and subjected to in vitro anticancer and antibacterial screening. Additionally, computational studies, such as DFT calculations and molecular docking analyses, were conducted.