To simplify the expression \( 2(-4c - 3) + 6(10c + 5) \), follow these steps:
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Distribute the \( 2 \) into the first term: \[ 2(-4c) + 2(-3) = -8c - 6 \]
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Distribute the \( 6 \) into the second term: \[ 6(10c) + 6(5) = 60c + 30 \]
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Combine the results from steps 1 and 2: \[ -8c - 6 + 60c + 30 \]
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Combine like terms (the terms with \( c \) and the constant terms):
- For the \( c \) terms: \( -8c + 60c = 52c \)
- For the constant terms: \( -6 + 30 = 24 \)
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Putting it all together: \[ 52c + 24 \]
So, the simplified expression is \( \boxed{52c + 24} \).