Answer
$$-8x^3+18x^2+23x-15
.$$
Work Step by Step
By multiplying each term in the first polynomial by each term in the second polynomial and combining the like terms, we get:
$$
(-2x^2 + 7x - 3)(4x + 5)=4x(-2x^2 + 7x - 3)+5(-2x^2 + 7x - 3)\\
=-8x^3+28x^2-12x-10x^2+35x-15\\
=-8x^3+18x^2+23x-15
.$$
