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Simplifying (3x + -1)(3x + -1) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: (-1 + 3x)(3x + -1) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: (-1 + 3x)(-1 + 3x) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Multiply (-1 + 3x) * (-1 + 3x) (-1(-1 + 3x) + 3x * (-1 + 3x)) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) ((1 + -3x) + 3x * (-1 + 3x)) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) (1 + -3x + (-1 * 3x + 3x * 3x)) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) (1 + -3x + (-3x + 9x2)) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Combine like terms: -3x + -3x = -6x (1 + -6x + 9x2) + -1(2x + 3)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: 1 + -6x + 9x2 + -1(3 + 2x)(2x + 3) = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: 1 + -6x + 9x2 + -1(3 + 2x)(3 + 2x) = 5(x + -2) + (x + -1)(5x + 2) Multiply (3 + 2x) * (3 + 2x) 1 + -6x + 9x2 + -1(3(3 + 2x) + 2x * (3 + 2x)) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + -1((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + -1((9 + 6x) + 2x * (3 + 2x)) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + -1(9 + 6x + (3 * 2x + 2x * 2x)) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + -1(9 + 6x + (6x + 4x2)) = 5(x + -2) + (x + -1)(5x + 2) Combine like terms: 6x + 6x = 12x 1 + -6x + 9x2 + -1(9 + 12x + 4x2) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + (9 * -1 + 12x * -1 + 4x2 * -1) = 5(x + -2) + (x + -1)(5x + 2) 1 + -6x + 9x2 + (-9 + -12x + -4x2) = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: 1 + -9 + -6x + -12x + 9x2 + -4x2 = 5(x + -2) + (x + -1)(5x + 2) Combine like terms: 1 + -9 = -8 -8 + -6x + -12x + 9x2 + -4x2 = 5(x + -2) + (x + -1)(5x + 2) Combine like terms: -6x + -12x = -18x -8 + -18x + 9x2 + -4x2 = 5(x + -2) + (x + -1)(5x + 2) Combine like terms: 9x2 + -4x2 = 5x2 -8 + -18x + 5x2 = 5(x + -2) + (x + -1)(5x + 2) Reorder the terms: -8 + -18x + 5x2 = 5(-2 + x) + (x + -1)(5x + 2) -8 + -18x + 5x2 = (-2 * 5 + x * 5) + (x + -1)(5x + 2) -8 + -18x + 5x2 = (-10 + 5x) + (x + -1)(5x + 2) Reorder the terms: -8 + -18x + 5x2 = -10 + 5x + (-1 + x)(5x + 2) Reorder the terms: -8 + -18x + 5x2 = -10 + 5x + (-1 + x)(2 + 5x) Multiply (-1 + x) * (2 + 5x) -8 + -18x + 5x2 = -10 + 5x + (-1(2 + 5x) + x(2 + 5x)) -8 + -18x + 5x2 = -10 + 5x + ((2 * -1 + 5x * -1) + x(2 + 5x)) -8 + -18x + 5x2 = -10 + 5x + ((-2 + -5x) + x(2 + 5x)) -8 + -18x + 5x2 = -10 + 5x + (-2 + -5x + (2 * x + 5x * x)) -8 + -18x + 5x2 = -10 + 5x + (-2 + -5x + (2x + 5x2)) Combine like terms: -5x + 2x = -3x -8 + -18x + 5x2 = -10 + 5x + (-2 + -3x + 5x2) Reorder the terms: -8 + -18x + 5x2 = -10 + -2 + 5x + -3x + 5x2 Combine like terms: -10 + -2 = -12 -8 + -18x + 5x2 = -12 + 5x + -3x + 5x2 Combine like terms: 5x + -3x = 2x -8 + -18x + 5x2 = -12 + 2x + 5x2 Add '-5x2' to each side of the equation. -8 + -18x + 5x2 + -5x2 = -12 + 2x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8 + -18x + 0 = -12 + 2x + 5x2 + -5x2 -8 + -18x = -12 + 2x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8 + -18x = -12 + 2x + 0 -8 + -18x = -12 + 2x Solving -8 + -18x = -12 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -8 + -18x + -2x = -12 + 2x + -2x Combine like terms: -18x + -2x = -20x -8 + -20x = -12 + 2x + -2x Combine like terms: 2x + -2x = 0 -8 + -20x = -12 + 0 -8 + -20x = -12 Add '8' to each side of the equation. -8 + 8 + -20x = -12 + 8 Combine like terms: -8 + 8 = 0 0 + -20x = -12 + 8 -20x = -12 + 8 Combine like terms: -12 + 8 = -4 -20x = -4 Divide each side by '-20'. x = 0.2 Simplifying x = 0.2
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