The problem requires us to simplify the expression $(a-5)(4+a)(3-2a)$ by first multiplying two of the binomials and then multiplying the result by the third binomial.

1. Problem Description

The problem requires us to simplify the expression $(a-5)(4+a)(3-2a)$ by first multiplying two of the binomials and then multiplying the result by the third binomial.

2. Solution Steps

We can first multiply $(a-5)$ and $(4+a)$:

$(a-5)(4+a) = a(4) + a(a) - 5(4) - 5(a) = 4a + a^2 - 20 - 5a = a^2 - a - 20$.

Now we multiply this result by $(3-2a)$:

$(a^2 - a - 20)(3-2a) = a^2(3) + a^2(-2a) - a(3) - a(-2a) - 20(3) - 20(-2a) = 3a^2 - 2a^3 - 3a + 2a^2 - 60 + 40a$.

Combining like terms, we have:

$-2a^3 + (3a^2 + 2a^2) + (-3a + 40a) - 60 = -2a^3 + 5a^2 + 37a - 60$.

So, $(a-5)(4+a)(3-2a) = -2a^3 + 5a^2 + 37a - 60$.

3. Final Answer

-2a^3+5a^2+37a-60