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Simplifying (3x + 1)(5x + -1) = (5x + 2)(3x + -4) + -7x Reorder the terms: (1 + 3x)(5x + -1) = (5x + 2)(3x + -4) + -7x Reorder the terms: (1 + 3x)(-1 + 5x) = (5x + 2)(3x + -4) + -7x Multiply (1 + 3x) * (-1 + 5x) (1(-1 + 5x) + 3x * (-1 + 5x)) = (5x + 2)(3x + -4) + -7x ((-1 * 1 + 5x * 1) + 3x * (-1 + 5x)) = (5x + 2)(3x + -4) + -7x ((-1 + 5x) + 3x * (-1 + 5x)) = (5x + 2)(3x + -4) + -7x (-1 + 5x + (-1 * 3x + 5x * 3x)) = (5x + 2)(3x + -4) + -7x (-1 + 5x + (-3x + 15x2)) = (5x + 2)(3x + -4) + -7x Combine like terms: 5x + -3x = 2x (-1 + 2x + 15x2) = (5x + 2)(3x + -4) + -7x Reorder the terms: -1 + 2x + 15x2 = (2 + 5x)(3x + -4) + -7x Reorder the terms: -1 + 2x + 15x2 = (2 + 5x)(-4 + 3x) + -7x Multiply (2 + 5x) * (-4 + 3x) -1 + 2x + 15x2 = (2(-4 + 3x) + 5x * (-4 + 3x)) + -7x -1 + 2x + 15x2 = ((-4 * 2 + 3x * 2) + 5x * (-4 + 3x)) + -7x -1 + 2x + 15x2 = ((-8 + 6x) + 5x * (-4 + 3x)) + -7x -1 + 2x + 15x2 = (-8 + 6x + (-4 * 5x + 3x * 5x)) + -7x -1 + 2x + 15x2 = (-8 + 6x + (-20x + 15x2)) + -7x Combine like terms: 6x + -20x = -14x -1 + 2x + 15x2 = (-8 + -14x + 15x2) + -7x Reorder the terms: -1 + 2x + 15x2 = -8 + -14x + -7x + 15x2 Combine like terms: -14x + -7x = -21x -1 + 2x + 15x2 = -8 + -21x + 15x2 Add '-15x2' to each side of the equation. -1 + 2x + 15x2 + -15x2 = -8 + -21x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -1 + 2x + 0 = -8 + -21x + 15x2 + -15x2 -1 + 2x = -8 + -21x + 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -1 + 2x = -8 + -21x + 0 -1 + 2x = -8 + -21x Solving -1 + 2x = -8 + -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. -1 + 2x + 21x = -8 + -21x + 21x Combine like terms: 2x + 21x = 23x -1 + 23x = -8 + -21x + 21x Combine like terms: -21x + 21x = 0 -1 + 23x = -8 + 0 -1 + 23x = -8 Add '1' to each side of the equation. -1 + 1 + 23x = -8 + 1 Combine like terms: -1 + 1 = 0 0 + 23x = -8 + 1 23x = -8 + 1 Combine like terms: -8 + 1 = -7 23x = -7 Divide each side by '23'. x = -0.3043478261 Simplifying x = -0.3043478261
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