a(4a-5)(2a+3)

To simplify the expression \( a(4a - 5)(2a + 3) \), we will first expand the product of the two binomials \( (4a - 5)(2a + 3) \).

1. Start by using the distributive property (FOIL method): \[ (4a - 5)(2a + 3) = 4a \cdot 2a + 4a \cdot 3 - 5 \cdot 2a - 5 \cdot 3 \] \[ = 8a^2 + 12a - 10a - 15 \]

2. Combine like terms: \[ 8a^2 + (12a - 10a) - 15 = 8a^2 + 2a - 15 \]

3. Now, we can multiply this result by \( a \): \[ a(8a^2 + 2a - 15) = 8a^3 + 2a^2 - 15a \]

So, the final simplified expression is:

\[ \boxed{8a^3 + 2a^2 - 15a} \]