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Simplifying (3x + -5)(6x + -7) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) Reorder the terms: (-5 + 3x)(6x + -7) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) Reorder the terms: (-5 + 3x)(-7 + 6x) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) Multiply (-5 + 3x) * (-7 + 6x) (-5(-7 + 6x) + 3x * (-7 + 6x)) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) ((-7 * -5 + 6x * -5) + 3x * (-7 + 6x)) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) ((35 + -30x) + 3x * (-7 + 6x)) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) (35 + -30x + (-7 * 3x + 6x * 3x)) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) (35 + -30x + (-21x + 18x2)) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) Combine like terms: -30x + -21x = -51x (35 + -51x + 18x2) = (3x + 2)(9x + -13) + -1(3x + 1)(3x + -1) Reorder the terms: 35 + -51x + 18x2 = (2 + 3x)(9x + -13) + -1(3x + 1)(3x + -1) Reorder the terms: 35 + -51x + 18x2 = (2 + 3x)(-13 + 9x) + -1(3x + 1)(3x + -1) Multiply (2 + 3x) * (-13 + 9x) 35 + -51x + 18x2 = (2(-13 + 9x) + 3x * (-13 + 9x)) + -1(3x + 1)(3x + -1) 35 + -51x + 18x2 = ((-13 * 2 + 9x * 2) + 3x * (-13 + 9x)) + -1(3x + 1)(3x + -1) 35 + -51x + 18x2 = ((-26 + 18x) + 3x * (-13 + 9x)) + -1(3x + 1)(3x + -1) 35 + -51x + 18x2 = (-26 + 18x + (-13 * 3x + 9x * 3x)) + -1(3x + 1)(3x + -1) 35 + -51x + 18x2 = (-26 + 18x + (-39x + 27x2)) + -1(3x + 1)(3x + -1) Combine like terms: 18x + -39x = -21x 35 + -51x + 18x2 = (-26 + -21x + 27x2) + -1(3x + 1)(3x + -1) Reorder the terms: 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(1 + 3x)(3x + -1) Reorder the terms: 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(1 + 3x)(-1 + 3x) Multiply (1 + 3x) * (-1 + 3x) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(1(-1 + 3x) + 3x * (-1 + 3x)) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1((-1 * 1 + 3x * 1) + 3x * (-1 + 3x)) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1((-1 + 3x) + 3x * (-1 + 3x)) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(-1 + 3x + (-1 * 3x + 3x * 3x)) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(-1 + 3x + (-3x + 9x2)) Combine like terms: 3x + -3x = 0 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(-1 + 0 + 9x2) 35 + -51x + 18x2 = -26 + -21x + 27x2 + -1(-1 + 9x2) 35 + -51x + 18x2 = -26 + -21x + 27x2 + (-1 * -1 + 9x2 * -1) 35 + -51x + 18x2 = -26 + -21x + 27x2 + (1 + -9x2) Reorder the terms: 35 + -51x + 18x2 = -26 + 1 + -21x + 27x2 + -9x2 Combine like terms: -26 + 1 = -25 35 + -51x + 18x2 = -25 + -21x + 27x2 + -9x2 Combine like terms: 27x2 + -9x2 = 18x2 35 + -51x + 18x2 = -25 + -21x + 18x2 Add '-18x2' to each side of the equation. 35 + -51x + 18x2 + -18x2 = -25 + -21x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 35 + -51x + 0 = -25 + -21x + 18x2 + -18x2 35 + -51x = -25 + -21x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 35 + -51x = -25 + -21x + 0 35 + -51x = -25 + -21x Solving 35 + -51x = -25 + -21x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21x' to each side of the equation. 35 + -51x + 21x = -25 + -21x + 21x Combine like terms: -51x + 21x = -30x 35 + -30x = -25 + -21x + 21x Combine like terms: -21x + 21x = 0 35 + -30x = -25 + 0 35 + -30x = -25 Add '-35' to each side of the equation. 35 + -35 + -30x = -25 + -35 Combine like terms: 35 + -35 = 0 0 + -30x = -25 + -35 -30x = -25 + -35 Combine like terms: -25 + -35 = -60 -30x = -60 Divide each side by '-30'. x = 2 Simplifying x = 2
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