To simplify the expression $2(-4c - 3) + 6(10c + 5)$, follow these steps:

1. Distribute the 2 to both terms inside the first parentheses: $2(-4c) + 2(-3) = -8c - 6$

2. Distribute the 6 to both terms inside the second parentheses: $6(10c) + 6(5) = 60c + 30$

3. Combine the simplified expressions: $-8c - 6 + 60c + 30$

4. Combine like terms: $(-8c + 60c) + (-6 + 30) = 52c + 24$

So, the simplified expression is: $52c + 24$

Would you like a detailed explanation or have any questions? Here are some related questions you might find useful:

1. How do you distribute a coefficient over terms inside parentheses?
2. What are like terms, and how do you combine them?
3. How do you simplify expressions involving both positive and negative coefficients?
4. Can you solve for $c$ in a similar equation?
5. How does distribution differ from factoring?

Tip: Always distribute multiplication across addition or subtraction inside parentheses before combining like terms.