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Simplifying (5x + -3)(2x + 7) + (2x + -7)(3 + -5x) = 0 Reorder the terms: (-3 + 5x)(2x + 7) + (2x + -7)(3 + -5x) = 0 Reorder the terms: (-3 + 5x)(7 + 2x) + (2x + -7)(3 + -5x) = 0 Multiply (-3 + 5x) * (7 + 2x) (-3(7 + 2x) + 5x * (7 + 2x)) + (2x + -7)(3 + -5x) = 0 ((7 * -3 + 2x * -3) + 5x * (7 + 2x)) + (2x + -7)(3 + -5x) = 0 ((-21 + -6x) + 5x * (7 + 2x)) + (2x + -7)(3 + -5x) = 0 (-21 + -6x + (7 * 5x + 2x * 5x)) + (2x + -7)(3 + -5x) = 0 (-21 + -6x + (35x + 10x2)) + (2x + -7)(3 + -5x) = 0 Combine like terms: -6x + 35x = 29x (-21 + 29x + 10x2) + (2x + -7)(3 + -5x) = 0 Reorder the terms: -21 + 29x + 10x2 + (-7 + 2x)(3 + -5x) = 0 Multiply (-7 + 2x) * (3 + -5x) -21 + 29x + 10x2 + (-7(3 + -5x) + 2x * (3 + -5x)) = 0 -21 + 29x + 10x2 + ((3 * -7 + -5x * -7) + 2x * (3 + -5x)) = 0 -21 + 29x + 10x2 + ((-21 + 35x) + 2x * (3 + -5x)) = 0 -21 + 29x + 10x2 + (-21 + 35x + (3 * 2x + -5x * 2x)) = 0 -21 + 29x + 10x2 + (-21 + 35x + (6x + -10x2)) = 0 Combine like terms: 35x + 6x = 41x -21 + 29x + 10x2 + (-21 + 41x + -10x2) = 0 Reorder the terms: -21 + -21 + 29x + 41x + 10x2 + -10x2 = 0 Combine like terms: -21 + -21 = -42 -42 + 29x + 41x + 10x2 + -10x2 = 0 Combine like terms: 29x + 41x = 70x -42 + 70x + 10x2 + -10x2 = 0 Combine like terms: 10x2 + -10x2 = 0 -42 + 70x + 0 = 0 -42 + 70x = 0 Solving -42 + 70x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + 70x = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 70x = 0 + 42 70x = 0 + 42 Combine like terms: 0 + 42 = 42 70x = 42 Divide each side by '70'. x = 0.6 Simplifying x = 0.6
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