A search for neutrinoless double-beta decay (0vBB) is performed using 36.55 g of the isotope Nd-150 with 5.25 y of data from the NEMO experiment. A complete background model for this source foil is constructed using a binned likelihood fit across several observables in multiple control channels. The 2vBB decay half-life is measured to be T(2v) = 9.34 +/- 0.22 (stat.) [+0.60, -0.59] (syst.) x 10^18 y, which represents the most precise measurement for this isotope to date. A multivariate analysis is performed in the search for 0vBB decay. As no evidence for 0vBB decay is observed, lower limits are obtained on the half-lives for several underlying beyond standard model mechanisms. The observed lower limit assuming a light Majorana neutrino exchange is T(0v) > 18.96 x 10^21 y at 90% CL, corresponding to an upper limit on the effective neutrino mass of < (2.64--8.64) eV, representing the most stringent limit obtained with the isotope Nd-150.