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Simplifying (2x + -1(-2))(3x + (-2)) = 6 + -1(-1 + -3x)(2x + 3) Multiply -1 * -2 (2x + 2)(3x + (-2)) = 6 + -1(-1 + -3x)(2x + 3) Reorder the terms: (2 + 2x)(3x + (-2)) = 6 + -1(-1 + -3x)(2x + 3) (2 + 2x)(3x + -2) = 6 + -1(-1 + -3x)(2x + 3) Reorder the terms: (2 + 2x)(-2 + 3x) = 6 + -1(-1 + -3x)(2x + 3) Multiply (2 + 2x) * (-2 + 3x) (2(-2 + 3x) + 2x * (-2 + 3x)) = 6 + -1(-1 + -3x)(2x + 3) ((-2 * 2 + 3x * 2) + 2x * (-2 + 3x)) = 6 + -1(-1 + -3x)(2x + 3) ((-4 + 6x) + 2x * (-2 + 3x)) = 6 + -1(-1 + -3x)(2x + 3) (-4 + 6x + (-2 * 2x + 3x * 2x)) = 6 + -1(-1 + -3x)(2x + 3) (-4 + 6x + (-4x + 6x2)) = 6 + -1(-1 + -3x)(2x + 3) Combine like terms: 6x + -4x = 2x (-4 + 2x + 6x2) = 6 + -1(-1 + -3x)(2x + 3) Reorder the terms: -4 + 2x + 6x2 = 6 + -1(-1 + -3x)(3 + 2x) Multiply (-1 + -3x) * (3 + 2x) -4 + 2x + 6x2 = 6 + -1(-1(3 + 2x) + -3x * (3 + 2x)) -4 + 2x + 6x2 = 6 + -1((3 * -1 + 2x * -1) + -3x * (3 + 2x)) -4 + 2x + 6x2 = 6 + -1((-3 + -2x) + -3x * (3 + 2x)) -4 + 2x + 6x2 = 6 + -1(-3 + -2x + (3 * -3x + 2x * -3x)) -4 + 2x + 6x2 = 6 + -1(-3 + -2x + (-9x + -6x2)) Combine like terms: -2x + -9x = -11x -4 + 2x + 6x2 = 6 + -1(-3 + -11x + -6x2) -4 + 2x + 6x2 = 6 + (-3 * -1 + -11x * -1 + -6x2 * -1) -4 + 2x + 6x2 = 6 + (3 + 11x + 6x2) Combine like terms: 6 + 3 = 9 -4 + 2x + 6x2 = 9 + 11x + 6x2 Add '-6x2' to each side of the equation. -4 + 2x + 6x2 + -6x2 = 9 + 11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 2x + 0 = 9 + 11x + 6x2 + -6x2 -4 + 2x = 9 + 11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 2x = 9 + 11x + 0 -4 + 2x = 9 + 11x Solving -4 + 2x = 9 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. -4 + 2x + -11x = 9 + 11x + -11x Combine like terms: 2x + -11x = -9x -4 + -9x = 9 + 11x + -11x Combine like terms: 11x + -11x = 0 -4 + -9x = 9 + 0 -4 + -9x = 9 Add '4' to each side of the equation. -4 + 4 + -9x = 9 + 4 Combine like terms: -4 + 4 = 0 0 + -9x = 9 + 4 -9x = 9 + 4 Combine like terms: 9 + 4 = 13 -9x = 13 Divide each side by '-9'. x = -1.444444444 Simplifying x = -1.444444444
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