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Simplifying (x + -3)(2 + -1x) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) Reorder the terms: (-3 + x)(2 + -1x) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) Multiply (-3 + x) * (2 + -1x) (-3(2 + -1x) + x(2 + -1x)) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) ((2 * -3 + -1x * -3) + x(2 + -1x)) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) ((-6 + 3x) + x(2 + -1x)) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) (-6 + 3x + (2 * x + -1x * x)) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) (-6 + 3x + (2x + -1x2)) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) Combine like terms: 3x + 2x = 5x (-6 + 5x + -1x2) + -1(x + -5)(5 + x) = -2x(x + -6) + -5(x + -1) Reorder the terms: -6 + 5x + -1x2 + -1(-5 + x)(5 + x) = -2x(x + -6) + -5(x + -1) Multiply (-5 + x) * (5 + x) -6 + 5x + -1x2 + -1(-5(5 + x) + x(5 + x)) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + -1((5 * -5 + x * -5) + x(5 + x)) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + -1((-25 + -5x) + x(5 + x)) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + -1(-25 + -5x + (5 * x + x * x)) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + -1(-25 + -5x + (5x + x2)) = -2x(x + -6) + -5(x + -1) Combine like terms: -5x + 5x = 0 -6 + 5x + -1x2 + -1(-25 + 0 + x2) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + -1(-25 + x2) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + (-25 * -1 + x2 * -1) = -2x(x + -6) + -5(x + -1) -6 + 5x + -1x2 + (25 + -1x2) = -2x(x + -6) + -5(x + -1) Reorder the terms: -6 + 25 + 5x + -1x2 + -1x2 = -2x(x + -6) + -5(x + -1) Combine like terms: -6 + 25 = 19 19 + 5x + -1x2 + -1x2 = -2x(x + -6) + -5(x + -1) Combine like terms: -1x2 + -1x2 = -2x2 19 + 5x + -2x2 = -2x(x + -6) + -5(x + -1) Reorder the terms: 19 + 5x + -2x2 = -2x(-6 + x) + -5(x + -1) 19 + 5x + -2x2 = (-6 * -2x + x * -2x) + -5(x + -1) 19 + 5x + -2x2 = (12x + -2x2) + -5(x + -1) Reorder the terms: 19 + 5x + -2x2 = 12x + -2x2 + -5(-1 + x) 19 + 5x + -2x2 = 12x + -2x2 + (-1 * -5 + x * -5) 19 + 5x + -2x2 = 12x + -2x2 + (5 + -5x) Reorder the terms: 19 + 5x + -2x2 = 5 + 12x + -5x + -2x2 Combine like terms: 12x + -5x = 7x 19 + 5x + -2x2 = 5 + 7x + -2x2 Add '2x2' to each side of the equation. 19 + 5x + -2x2 + 2x2 = 5 + 7x + -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 19 + 5x + 0 = 5 + 7x + -2x2 + 2x2 19 + 5x = 5 + 7x + -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 19 + 5x = 5 + 7x + 0 19 + 5x = 5 + 7x Solving 19 + 5x = 5 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 19 + 5x + -7x = 5 + 7x + -7x Combine like terms: 5x + -7x = -2x 19 + -2x = 5 + 7x + -7x Combine like terms: 7x + -7x = 0 19 + -2x = 5 + 0 19 + -2x = 5 Add '-19' to each side of the equation. 19 + -19 + -2x = 5 + -19 Combine like terms: 19 + -19 = 0 0 + -2x = 5 + -19 -2x = 5 + -19 Combine like terms: 5 + -19 = -14 -2x = -14 Divide each side by '-2'. x = 7 Simplifying x = 7
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