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Simplifying (6x + 7)(x + 8) = (2x + 9)(3x + -5) Reorder the terms: (7 + 6x)(x + 8) = (2x + 9)(3x + -5) Reorder the terms: (7 + 6x)(8 + x) = (2x + 9)(3x + -5) Multiply (7 + 6x) * (8 + x) (7(8 + x) + 6x * (8 + x)) = (2x + 9)(3x + -5) ((8 * 7 + x * 7) + 6x * (8 + x)) = (2x + 9)(3x + -5) ((56 + 7x) + 6x * (8 + x)) = (2x + 9)(3x + -5) (56 + 7x + (8 * 6x + x * 6x)) = (2x + 9)(3x + -5) (56 + 7x + (48x + 6x2)) = (2x + 9)(3x + -5) Combine like terms: 7x + 48x = 55x (56 + 55x + 6x2) = (2x + 9)(3x + -5) Reorder the terms: 56 + 55x + 6x2 = (9 + 2x)(3x + -5) Reorder the terms: 56 + 55x + 6x2 = (9 + 2x)(-5 + 3x) Multiply (9 + 2x) * (-5 + 3x) 56 + 55x + 6x2 = (9(-5 + 3x) + 2x * (-5 + 3x)) 56 + 55x + 6x2 = ((-5 * 9 + 3x * 9) + 2x * (-5 + 3x)) 56 + 55x + 6x2 = ((-45 + 27x) + 2x * (-5 + 3x)) 56 + 55x + 6x2 = (-45 + 27x + (-5 * 2x + 3x * 2x)) 56 + 55x + 6x2 = (-45 + 27x + (-10x + 6x2)) Combine like terms: 27x + -10x = 17x 56 + 55x + 6x2 = (-45 + 17x + 6x2) Add '-6x2' to each side of the equation. 56 + 55x + 6x2 + -6x2 = -45 + 17x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 56 + 55x + 0 = -45 + 17x + 6x2 + -6x2 56 + 55x = -45 + 17x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 56 + 55x = -45 + 17x + 0 56 + 55x = -45 + 17x Solving 56 + 55x = -45 + 17x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17x' to each side of the equation. 56 + 55x + -17x = -45 + 17x + -17x Combine like terms: 55x + -17x = 38x 56 + 38x = -45 + 17x + -17x Combine like terms: 17x + -17x = 0 56 + 38x = -45 + 0 56 + 38x = -45 Add '-56' to each side of the equation. 56 + -56 + 38x = -45 + -56 Combine like terms: 56 + -56 = 0 0 + 38x = -45 + -56 38x = -45 + -56 Combine like terms: -45 + -56 = -101 38x = -101 Divide each side by '38'. x = -2.657894737 Simplifying x = -2.657894737
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