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We report the first amplitude analysis 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 3.773 GeV, 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+2.5−0.8stat.±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.