Expanding the expression, we get:

(3a-2)(a^2-a+1) - (6a^5-10a^4)/(2a^2)
= 3a(a^2) - 3a(a) + 3a - 2(a^2) + 2a - 2 - (3a^4 - 5a^3)
= 3a^3 - 3a^2 + 3a - 2a^2 + 2a - 2 - (3a^4 - 5a^3)
= 3a^3 - 5a^2 + 5a - 2 - 3a^4 + 5a^3
= -3a^4 + 8a^3 - 5a^2 + 5a - 2