To solve the expression \((-6x^2 + 5x - 7) + (3x^2 - 5x)\), let's simplify step by step by combining like terms.

1. **Group like terms:**
   \[
   (-6x^2 + 3x^2) + (5x - 5x) - 7
   \]

2. **Simplify:**
   \[
   -3x^2 + 0x - 7
   \]

3. **Final result:**
   \[
   -3x^2 - 7
   \]

So, the simplified expression is \(-3x^2 - 7\).

Would you like any more details or clarification?

Here are some related questions for further practice:
1. Simplify: \((2x^2 - 3x + 4) + (-x^2 + 5x - 6)\)
2. Simplify: \((4x^2 + 6x - 9) - (2x^2 - 3x + 4)\)
3. Solve for \(x\): \(-3x^2 - 7 = 0\)
4. Expand: \((x - 2)(3x + 4)\)
5. Factor: \(-3x^2 - 7\)

**Tip:** When combining like terms, always align terms based on their degree (e.g., all \(x^2\) terms together, all \(x\) terms together, and constant terms together).

Learn how to simplify the polynomial expression (-6x² + 5x - 7) + (3x² - 5x) by combining like terms. This step-by-step solution covers key algebraic concepts such as simplifying polynomials and using the distributive property. Suitable for students in Grades 7-9.

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