We report the first amplitude analyses of the decays D0→π+π-η and D+→π+π0η using a data sample taken with the BESIII detector at the center-of-mass energy of 3773 MeV, corresponding to an integrated luminosity of 7.9 fb-1. The contribution from the process D0(+)→a0(980)+π-(0) is significantly larger than the D0(+)→a0(980)-(0)π+ contribution. The ratios B(D0→a0(980)+π-)/B(D0→a0(980)-π+) and B(D+→a0(980)+π0)/B(D+→a0(980)0π+) are measured to be 7.5-0.8stat+2.5±1.7syst and 2.6±0.6stat±0.3syst, respectively. The measured D0 ratio disagrees with the theoretical predictions by orders of magnitudes, thus implying a substantial contribution from final-state interactions.