Let's perform the operation step by step.
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Expand the product \(- (2x + 6)(3x + 4)\): \[ (2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4 \] \[ = 6x^2 + 8x + 18x + 24 \] \[ = 6x^2 + 26x + 24 \]
Now, applying the negative sign: \[
- (6x^2 + 26x + 24) = -6x^2 - 26x - 24 \]
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Combine this with the remaining terms \(5x^2 - 7x\): \[
- 6x^2 - 26x - 24 + 5x^2 - 7x \]
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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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Final expression: \[ -x^2 - 33x - 24 \]
Thus, the simplified expression is: \[ \boxed{-x^2 - 33x - 24} \]