The problem asks us to factor out the greatest common factor from the expression $8b(a-3b) + 7(-3b+a)$.

1. Problem Description

The problem asks us to factor out the greatest common factor from the expression $8b(a-3b) + 7(-3b+a)$.

2. Solution Steps

We are given the expression $8b(a-3b) + 7(-3b+a)$.

Notice that the term $(a-3b)$ appears in both parts of the expression.

We can rewrite the second term as $7(a-3b)$.

So the expression becomes $8b(a-3b) + 7(a-3b)$.

Now, we can factor out the common factor $(a-3b)$ from both terms.

$(a-3b)$ is multiplied by $8b$ in the first term and by $7$ in the second term.

Therefore, we can write the expression as $(a-3b)(8b+7)$.

3. Final Answer

$(a-3b)(8b+7)$