#### Answer

$$(2x - 3)(2x + 5)$$

#### Work Step by Step

We want to use the factorization method by grouping.
First, we want to multiply the leading coefficient $a$ with the constant $c$:
$$(4)(-15) = -60$$
Now, we find the factors of $ac$ that sum up to $b$. Here are the factors:
$-60$ and $1$ or $60$ and $-1$
$-15$ and $4$ or $15$ and $-4$
$-20$ and $3$ or $20$ and $-3$
$-10$ and $6$ or $10$ and $-6$
$-30$ and $2$ or $30$ and $-2$
$-12$ and $5$ or $12$ and $-5$
The factors that sum up to $b$ would be $10$ and $-6$.
We can now rewrite the middle term as the difference of the two factors:
$$4x^2 + (10x - 6x) - 15$$
We can now group them together:
$$(4x^2 + 10x) + (-6x - 15)$$
We factor out the common factor for each binomial group:
$$2x(2x + 5) - 3(2x + 5)$$
Now we factor by grouping:
$$(2x - 3)(2x + 5)$$