Let's simplify the expression step by step.
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Start with the expression: \[ 4\left(\frac{3}{4}x + 3x - 2\right) - 2\left(3x^2 + 1 + 3x\right) \]
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Distribute \(4\) into the first term: \[ 4\left(\frac{3}{4}x\right) + 4(3x) + 4(-2) = 3x + 12x - 8 = 15x - 8 \]
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Now distribute \(-2\) into the second term: \[ -2(3x^2) - 2(1) - 2(3x) = -6x^2 - 2 - 6x \]
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Combine the results from both distributions: \[ (15x - 8) + (-6x^2 - 2 - 6x) \] This results in: \[ -6x^2 + 15x - 6x - 8 - 2 = -6x^2 + (15x - 6x) - 10 \] \[ = -6x^2 + 9x - 10 \]
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Rearranging the expression gives: \[ -6x^2 + 9x - 10 \]
Now, we can write this in the form \(Ax^2 + Bx + C\) as follows: \[ A = -6, \quad B = 9, \quad C = -10 \]
Thus, the answer for the expression in the form \(x^2 + x - \) is: \[ -6, \quad 9, \quad -10. \]
So, \[ \underline{-6} \quad \underline{9} \quad \underline{-10} \] are the values that fill in for the coefficients in the expression: \[ -6x^2 + 9x - 10. \]
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