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Simplifying (5x + 1)(x + -3) = (x + -5)(5x + -2) + 2 Reorder the terms: (1 + 5x)(x + -3) = (x + -5)(5x + -2) + 2 Reorder the terms: (1 + 5x)(-3 + x) = (x + -5)(5x + -2) + 2 Multiply (1 + 5x) * (-3 + x) (1(-3 + x) + 5x * (-3 + x)) = (x + -5)(5x + -2) + 2 ((-3 * 1 + x * 1) + 5x * (-3 + x)) = (x + -5)(5x + -2) + 2 ((-3 + 1x) + 5x * (-3 + x)) = (x + -5)(5x + -2) + 2 (-3 + 1x + (-3 * 5x + x * 5x)) = (x + -5)(5x + -2) + 2 (-3 + 1x + (-15x + 5x2)) = (x + -5)(5x + -2) + 2 Combine like terms: 1x + -15x = -14x (-3 + -14x + 5x2) = (x + -5)(5x + -2) + 2 Reorder the terms: -3 + -14x + 5x2 = (-5 + x)(5x + -2) + 2 Reorder the terms: -3 + -14x + 5x2 = (-5 + x)(-2 + 5x) + 2 Multiply (-5 + x) * (-2 + 5x) -3 + -14x + 5x2 = (-5(-2 + 5x) + x(-2 + 5x)) + 2 -3 + -14x + 5x2 = ((-2 * -5 + 5x * -5) + x(-2 + 5x)) + 2 -3 + -14x + 5x2 = ((10 + -25x) + x(-2 + 5x)) + 2 -3 + -14x + 5x2 = (10 + -25x + (-2 * x + 5x * x)) + 2 -3 + -14x + 5x2 = (10 + -25x + (-2x + 5x2)) + 2 Combine like terms: -25x + -2x = -27x -3 + -14x + 5x2 = (10 + -27x + 5x2) + 2 Reorder the terms: -3 + -14x + 5x2 = 10 + 2 + -27x + 5x2 Combine like terms: 10 + 2 = 12 -3 + -14x + 5x2 = 12 + -27x + 5x2 Add '-5x2' to each side of the equation. -3 + -14x + 5x2 + -5x2 = 12 + -27x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -3 + -14x + 0 = 12 + -27x + 5x2 + -5x2 -3 + -14x = 12 + -27x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -3 + -14x = 12 + -27x + 0 -3 + -14x = 12 + -27x Solving -3 + -14x = 12 + -27x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27x' to each side of the equation. -3 + -14x + 27x = 12 + -27x + 27x Combine like terms: -14x + 27x = 13x -3 + 13x = 12 + -27x + 27x Combine like terms: -27x + 27x = 0 -3 + 13x = 12 + 0 -3 + 13x = 12 Add '3' to each side of the equation. -3 + 3 + 13x = 12 + 3 Combine like terms: -3 + 3 = 0 0 + 13x = 12 + 3 13x = 12 + 3 Combine like terms: 12 + 3 = 15 13x = 15 Divide each side by '13'. x = 1.153846154 Simplifying x = 1.153846154
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