Let's simplify the expression step by step:
We start with the expression:
\[ -(2x + 6)(3x + 4) + 5x^2 - 7x \]
First, we need to expand \(-(2x + 6)(3x + 4)\):
\[ (2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4 \]
Calculating each term:
- \(2x \cdot 3x = 6x^2\)
- \(2x \cdot 4 = 8x\)
- \(6 \cdot 3x = 18x\)
- \(6 \cdot 4 = 24\)
Now, combine these results:
\[ (2x + 6)(3x + 4) = 6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24 \]
Now, apply the negative sign:
\[ -(2x + 6)(3x + 4) = -6x^2 - 26x - 24 \]
Next, we combine this with the rest of the expression:
\[ -6x^2 - 26x - 24 + 5x^2 - 7x \]
Combine like terms:
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For \(x^2\) terms: \(-6x^2 + 5x^2 = -x^2\)
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For \(x\) terms: \(-26x - 7x = -33x\)
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The constant term is: \(-24\)
Putting it all together gives:
\[ -x^2 - 33x - 24 \]
So, the fully simplified expression is:
\[ \boxed{-x^2 - 33x - 24} \]
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