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Simplifying (5x + -6)(x + 7) = (x + -14)(1 + -2x) Reorder the terms: (-6 + 5x)(x + 7) = (x + -14)(1 + -2x) Reorder the terms: (-6 + 5x)(7 + x) = (x + -14)(1 + -2x) Multiply (-6 + 5x) * (7 + x) (-6(7 + x) + 5x * (7 + x)) = (x + -14)(1 + -2x) ((7 * -6 + x * -6) + 5x * (7 + x)) = (x + -14)(1 + -2x) ((-42 + -6x) + 5x * (7 + x)) = (x + -14)(1 + -2x) (-42 + -6x + (7 * 5x + x * 5x)) = (x + -14)(1 + -2x) (-42 + -6x + (35x + 5x2)) = (x + -14)(1 + -2x) Combine like terms: -6x + 35x = 29x (-42 + 29x + 5x2) = (x + -14)(1 + -2x) Reorder the terms: -42 + 29x + 5x2 = (-14 + x)(1 + -2x) Multiply (-14 + x) * (1 + -2x) -42 + 29x + 5x2 = (-14(1 + -2x) + x(1 + -2x)) -42 + 29x + 5x2 = ((1 * -14 + -2x * -14) + x(1 + -2x)) -42 + 29x + 5x2 = ((-14 + 28x) + x(1 + -2x)) -42 + 29x + 5x2 = (-14 + 28x + (1 * x + -2x * x)) -42 + 29x + 5x2 = (-14 + 28x + (1x + -2x2)) Combine like terms: 28x + 1x = 29x -42 + 29x + 5x2 = (-14 + 29x + -2x2) Add '-29x' to each side of the equation. -42 + 29x + -29x + 5x2 = -14 + 29x + -29x + -2x2 Combine like terms: 29x + -29x = 0 -42 + 0 + 5x2 = -14 + 29x + -29x + -2x2 -42 + 5x2 = -14 + 29x + -29x + -2x2 Combine like terms: 29x + -29x = 0 -42 + 5x2 = -14 + 0 + -2x2 -42 + 5x2 = -14 + -2x2 Solving -42 + 5x2 = -14 + -2x2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2x2' to each side of the equation. -42 + 5x2 + 2x2 = -14 + -2x2 + 2x2 Combine like terms: 5x2 + 2x2 = 7x2 -42 + 7x2 = -14 + -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -42 + 7x2 = -14 + 0 -42 + 7x2 = -14 Add '42' to each side of the equation. -42 + 42 + 7x2 = -14 + 42 Combine like terms: -42 + 42 = 0 0 + 7x2 = -14 + 42 7x2 = -14 + 42 Combine like terms: -14 + 42 = 28 7x2 = 28 Divide each side by '7'. x2 = 4 Simplifying x2 = 4 Take the square root of each side: x = {-2, 2}
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