To solve the expression $(5x - 10)(3x + 15)$, we'll use the distributive property (also known as the FOIL method for binomials):

$(5x - 10)(3x + 15)$

Expanding each term:

1. First: $5x \times 3x = 15x^2$
2. Outer: $5x \times 15 = 75x$
3. Inner: $-10 \times 3x = -30x$
4. Last: $-10 \times 15 = -150$

Now, combine all these terms together:

$15x^2 + 75x - 30x - 150$

Combine like terms:

$15x^2 + 45x - 150$

So, the expanded form of $(5x - 10)(3x + 15)$ is:

$15x^2 + 45x - 150$

Would you like more details, or do you have any questions about this solution? Here are five related questions you might find helpful:

1. How do you factor out a common factor from the polynomial $15x^2 + 45x - 150$?
2. What is the significance of the distributive property in algebra?
3. How would you solve the equation if it was set equal to zero, like $(5x - 10)(3x + 15) = 0$?
4. Can you expand and simplify $(2x + 3)(4x - 5)$?
5. How do you solve quadratic equations after expanding binomials?

Tip: When expanding binomials, always ensure you combine like terms to simplify the expression fully.