Based on (2712.4±14.3)×106 ψ(3686) events, we investigate four hadronic decay modes of the P-wave charmonium spin-singlet state hc(1P1)→h+h-π0/η (h=π or K) via the process ψ(3686)→π0hc at BESIII. The hc→π+π-π0 decay is observed with a significance of 9.6σ after taking into account systematic uncertainties. Evidences for hc→K+K-π0 and hc→K+K-η are found with significances of 3.5σ and 3.3σ, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be B(hc→π+π-π0)=(1.36±0.16±0.14)×10-3, B(hc→K+K-π0)=(3.26±0.84±0.36)×10-4, and B(hc→K+K-η)=(3.13±1.08±0.38)×10-4, where the first uncertainties are statistical and the second are systematic. No significant signal of hc→π+π-η is found, and the upper limit of its decay branching fraction is determined to be B(hc→π+π-η)<4.0×10-4 at the 90% confidence level.