We report the first amplitude analyses of the decays D+-> pi(+)pi(-)eta and D+-> pi(+)pi(0)eta 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(+) -> a(0)(980)(+)pi(-(0)) is significantly larger than the D0(+) -> a(0)(980)(-(0))pi(+)contribution. The ratios B(D-0 -> a(0)(980)(+)pi(-)/B(D-0 -> a(0)(980)+pi(-)) and B(D+ -> a(0) (980)+pi(0))/ B(D+ -> a(0) (980)(0)pi(+)) are measured to be 7.5(-0.8stat)(+2.5) +/- 1.7(syst) and 2.6 +/- 0.6(stat) +/- 0.3(syst), respectively. The measured D-0 ratio disagrees with the theoretical predictions by orders of magnitudes, thus implying a substantial contribution from final-state interactions.