Let's solve the given expression step by step. The expression is:

$(-4x^2 + 3x - 10) + (3x^3 - 2x^2 + 7)$

1. First, remove the parentheses:

$-4x^2 + 3x - 10 + 3x^3 - 2x^2 + 7$

2. Now, combine like terms. Group terms with the same powers of $x$:

$3x^3 + (-4x^2 - 2x^2) + 3x + (-10 + 7)$

3. Simplify:

$3x^3 - 6x^2 + 3x - 3$

Thus, the result of the addition is:

$3x^3 - 6x^2 + 3x - 3$

Would you like more details or have any questions?

Here are some related questions:

1. How do you add or subtract polynomials?
2. What are like terms in algebraic expressions?
3. Can you explain how to factor polynomials?
4. How can we verify the solution to a polynomial equation?
5. What is the degree of the polynomial $3x^3 - 6x^2 + 3x - 3$?

Tip: When combining like terms, always check the powers of $x$ to make sure you're grouping them correctly.