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Simplifying (5x + 7)(3x + -8) = (5x + 4)(3x + 5) Reorder the terms: (7 + 5x)(3x + -8) = (5x + 4)(3x + 5) Reorder the terms: (7 + 5x)(-8 + 3x) = (5x + 4)(3x + 5) Multiply (7 + 5x) * (-8 + 3x) (7(-8 + 3x) + 5x * (-8 + 3x)) = (5x + 4)(3x + 5) ((-8 * 7 + 3x * 7) + 5x * (-8 + 3x)) = (5x + 4)(3x + 5) ((-56 + 21x) + 5x * (-8 + 3x)) = (5x + 4)(3x + 5) (-56 + 21x + (-8 * 5x + 3x * 5x)) = (5x + 4)(3x + 5) (-56 + 21x + (-40x + 15x2)) = (5x + 4)(3x + 5) Combine like terms: 21x + -40x = -19x (-56 + -19x + 15x2) = (5x + 4)(3x + 5) Reorder the terms: -56 + -19x + 15x2 = (4 + 5x)(3x + 5) Reorder the terms: -56 + -19x + 15x2 = (4 + 5x)(5 + 3x) Multiply (4 + 5x) * (5 + 3x) -56 + -19x + 15x2 = (4(5 + 3x) + 5x * (5 + 3x)) -56 + -19x + 15x2 = ((5 * 4 + 3x * 4) + 5x * (5 + 3x)) -56 + -19x + 15x2 = ((20 + 12x) + 5x * (5 + 3x)) -56 + -19x + 15x2 = (20 + 12x + (5 * 5x + 3x * 5x)) -56 + -19x + 15x2 = (20 + 12x + (25x + 15x2)) Combine like terms: 12x + 25x = 37x -56 + -19x + 15x2 = (20 + 37x + 15x2) Add '-15x2' to each side of the equation. -56 + -19x + 15x2 + -15x2 = 20 + 37x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -56 + -19x + 0 = 20 + 37x + 15x2 + -15x2 -56 + -19x = 20 + 37x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -56 + -19x = 20 + 37x + 0 -56 + -19x = 20 + 37x Solving -56 + -19x = 20 + 37x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37x' to each side of the equation. -56 + -19x + -37x = 20 + 37x + -37x Combine like terms: -19x + -37x = -56x -56 + -56x = 20 + 37x + -37x Combine like terms: 37x + -37x = 0 -56 + -56x = 20 + 0 -56 + -56x = 20 Add '56' to each side of the equation. -56 + 56 + -56x = 20 + 56 Combine like terms: -56 + 56 = 0 0 + -56x = 20 + 56 -56x = 20 + 56 Combine like terms: 20 + 56 = 76 -56x = 76 Divide each side by '-56'. x = -1.357142857 Simplifying x = -1.357142857
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