Search for Neutral B-Meson Decays to a0pi, a0K, etarho0, and etaf0

We present a search for B0 decays to charmless final states involving an eta meson, a charged pion and a second charged pion or kaon. The data sample corresponds to 383x10^6 BBbar pairs collected with the BABAR detector operating at the PEP-II asymmetric-energy B Factory at SLAC. We find no significant signals and determine the following 90% C.L. upper limits: BR(B->a0-pi+) x BR(a0- -> etapi-) < 3.1x10^-6, BR(B->a0-K+) x BR(a0- -> etapi-) < 1.9x10^-6, BR(B->a0(1450)-pi+) x BR(a0(1450)- -> etapi-) < 2.3x10^-6, BR(B->a0(1450)-K+) x BR(a0(1450)- -> etapi-) < 3.1x10^-6, BR(B->etarho0) < 1.5x10^-6, and BR(B->eta f0(980)) x BR(f0(980)- -> pi+pi-) < 0.4x10^-6.