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.

Learn how to simplify the polynomial expression x(-5x - 6) + (2x^2 + 8x + 9) through step-by-step instructions. This solution covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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