Let's solve the expression $x(-5x - 6) + (2x^2 + 8x + 9)$.

Step-by-step Solution:

1. Distribute $x$ in the first part: $x(-5x - 6) = -5x^2 - 6x$

2. Now substitute this back into the expression: $(-5x^2 - 6x) + (2x^2 + 8x + 9)$

3. Combine like terms: $(-5x^2 + 2x^2) + (-6x + 8x) + 9$ This simplifies to: $-3x^2 + 2x + 9$

Final answer:

$-3x^2 + 2x + 9$

Would you like any more details or further clarifications?

Here are 5 related questions to expand on this:

1. What are the properties of polynomials?
2. How do you factor quadratic expressions like $-3x^2 + 2x + 9$?
3. What is the degree of the polynomial $-3x^2 + 2x + 9$?
4. How do you solve quadratic equations using the quadratic formula?
5. How can you graph quadratic functions like $-3x^2 + 2x + 9$?

Tip: Always group like terms to simplify polynomial expressions efficiently.