  We report measurements of charmless hadronic B^0 decays into the pi+pi-K+pi+
final state. The analysis uses a sample of 657x10^6 BBbar pairs collected with
the Belle detector at the KEKB asymmetric-energy e+e- collider at the Y(4S)
resonance. The decay B^0 -> rho0 Kpi is observed for the first time; the
significance is 5.0sigma and the corresponding partial branching fraction for
M_Kpi in (0.75,1.20) GeV/c^2 is [2.8 +- 0.5(stat) +-0.5(syst)] x 10^{-6}. We
also obtain the first evidence for B^0 -> f0Kpi with 3.5sigma significance and
for B^0 -> pi+pi-K*0 with 4.5sigma significance. For the two-body decays B^0 ->
rho0K*0 and B^0 -> f0K*0, the significances are 2.7sigma and 2.5sigma,
respectively, and the upper limits on the branching fractions are 3.4x10^{-6}
and 2.2x10^{-6} at 90% confidence level.
