#### Answer

$$2a^3-5a^2-37a-30$$

#### Work Step by Step

To multiply out three binomials, we first multiply the first two like normal, giving us two binomials total. Next, we multiply out these two binomials, multiplying each term of one binomial by each term in the other binomial. Thus, we find:
$$\left(a-6\right)\left(2a+5\right)\left(a+1\right) \\ \left(2a^2-7a-30\right)\left(a+1\right) \\ 2a^3-5a^2-37a-30$$