The recent observation by the D0 collaboration of a narrow structure X(5568) consisting of four different quark flavors bdus, has not been confirmed by LHCb. More data and dedicated analyses are needed to cover a larger mass range. In the tightly bound diquark model, we estimate the lightest bdus, 0^+ tetraquark at a mass of about 5770 MeV, approximately 200 MeV above the reported X(5568), and just 7 MeV below the B Kbar threshold. The charged tetraquark is accompanied by I=1 and I=0 neutral partners almost degenerate in mass. A bdus, S-wave, 1^+ quartet at 5820 MeV is implied as well. In the charm sector, cdus, 0^+ and 1^+ tetraquarks are predicted at 2365 MeV and 2501 MeV, about 40-50 MeV heavier than D_{s0}(2317) and D_{s1}(2460). bdus tetraquarks can be searched in the hadronic debris of a jet initiated by a b. However, some of them may also be produced in B_c decays. The proposed discovery modes of S-wave tetraquarks are B_c --> X_{b0} + pi with the subsequent decays X_{b0} --> B_s + pi, giving rise to final states such as B_s pi^+ pi^0. We also emphasize the importance of B_c decays as a source of bound hidden charm tetraquarks, such as B_c --> X(3872) + pi.
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