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Simplifying (X + 1)(x + 2)(x + 3)(x + 4) = 15 Reorder the terms: (1 + X)(x + 2)(x + 3)(x + 4) = 15 Reorder the terms: (1 + X)(2 + x)(x + 3)(x + 4) = 15 Reorder the terms: (1 + X)(2 + x)(3 + x)(x + 4) = 15 Reorder the terms: (1 + X)(2 + x)(3 + x)(4 + x) = 15 Multiply (1 + X) * (2 + x) (1(2 + x) + X(2 + x))(3 + x)(4 + x) = 15 ((2 * 1 + x * 1) + X(2 + x))(3 + x)(4 + x) = 15 ((2 + 1x) + X(2 + x))(3 + x)(4 + x) = 15 (2 + 1x + (2 * X + x * X))(3 + x)(4 + x) = 15 (2 + 1x + (2X + xX))(3 + x)(4 + x) = 15 Reorder the terms: (2 + 2X + 1x + xX)(3 + x)(4 + x) = 15 (2 + 2X + 1x + xX)(3 + x)(4 + x) = 15 Multiply (2 + 2X + 1x + xX) * (3 + x) (2(3 + x) + 2X * (3 + x) + 1x * (3 + x) + xX(3 + x))(4 + x) = 15 ((3 * 2 + x * 2) + 2X * (3 + x) + 1x * (3 + x) + xX(3 + x))(4 + x) = 15 ((6 + 2x) + 2X * (3 + x) + 1x * (3 + x) + xX(3 + x))(4 + x) = 15 (6 + 2x + (3 * 2X + x * 2X) + 1x * (3 + x) + xX(3 + x))(4 + x) = 15 (6 + 2x + (6X + 2xX) + 1x * (3 + x) + xX(3 + x))(4 + x) = 15 (6 + 2x + 6X + 2xX + (3 * 1x + x * 1x) + xX(3 + x))(4 + x) = 15 (6 + 2x + 6X + 2xX + (3x + 1x2) + xX(3 + x))(4 + x) = 15 (6 + 2x + 6X + 2xX + 3x + 1x2 + (3 * xX + x * xX))(4 + x) = 15 (6 + 2x + 6X + 2xX + 3x + 1x2 + (3xX + x2X))(4 + x) = 15 Reorder the terms: (6 + 6X + 2x + 3x + 2xX + 3xX + 1x2 + x2X)(4 + x) = 15 Combine like terms: 2x + 3x = 5x (6 + 6X + 5x + 2xX + 3xX + 1x2 + x2X)(4 + x) = 15 Combine like terms: 2xX + 3xX = 5xX (6 + 6X + 5x + 5xX + 1x2 + x2X)(4 + x) = 15 Multiply (6 + 6X + 5x + 5xX + 1x2 + x2X) * (4 + x) (6(4 + x) + 6X * (4 + x) + 5x * (4 + x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 ((4 * 6 + x * 6) + 6X * (4 + x) + 5x * (4 + x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 ((24 + 6x) + 6X * (4 + x) + 5x * (4 + x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + (4 * 6X + x * 6X) + 5x * (4 + x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + (24X + 6xX) + 5x * (4 + x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + (4 * 5x + x * 5x) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + (20x + 5x2) + 5xX * (4 + x) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + (4 * 5xX + x * 5xX) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + (20xX + 5x2X) + 1x2 * (4 + x) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + 20xX + 5x2X + (4 * 1x2 + x * 1x2) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + 20xX + 5x2X + (4x2 + 1x3) + x2X(4 + x)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + 20xX + 5x2X + 4x2 + 1x3 + (4 * x2X + x * x2X)) = 15 (24 + 6x + 24X + 6xX + 20x + 5x2 + 20xX + 5x2X + 4x2 + 1x3 + (4x2X + x3X)) = 15 Reorder the terms: (24 + 24X + 6x + 20x + 6xX + 20xX + 5x2 + 4x2 + 5x2X + 4x2X + 1x3 + x3X) = 15 Combine like terms: 6x + 20x = 26x (24 + 24X + 26x + 6xX + 20xX + 5x2 + 4x2 + 5x2X + 4x2X + 1x3 + x3X) = 15 Combine like terms: 6xX + 20xX = 26xX (24 + 24X + 26x + 26xX + 5x2 + 4x2 + 5x2X + 4x2X + 1x3 + x3X) = 15 Combine like terms: 5x2 + 4x2 = 9x2 (24 + 24X + 26x + 26xX + 9x2 + 5x2X + 4x2X + 1x3 + x3X) = 15 Combine like terms: 5x2X + 4x2X = 9x2X (24 + 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X) = 15 Solving 24 + 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = 15 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + -24 + x3X = 15 + -24 Reorder the terms: 24 + -24 + 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = 15 + -24 Combine like terms: 24 + -24 = 0 0 + 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = 15 + -24 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = 15 + -24 Combine like terms: 15 + -24 = -9 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = -9 Add '-26x' to each side of the equation. 24X + 26x + 26xX + 9x2 + 9x2X + 1x3 + -26x + x3X = -9 + -26x Reorder the terms: 24X + 26x + -26x + 26xX + 9x2 + 9x2X + 1x3 + x3X = -9 + -26x Combine like terms: 26x + -26x = 0 24X + 0 + 26xX + 9x2 + 9x2X + 1x3 + x3X = -9 + -26x 24X + 26xX + 9x2 + 9x2X + 1x3 + x3X = -9 + -26x Add '-9x2' to each side of the equation. 24X + 26xX + 9x2 + 9x2X + 1x3 + -9x2 + x3X = -9 + -26x + -9x2 Reorder the terms: 24X + 26xX + 9x2 + -9x2 + 9x2X + 1x3 + x3X = -9 + -26x + -9x2 Combine like terms: 9x2 + -9x2 = 0 24X + 26xX + 0 + 9x2X + 1x3 + x3X = -9 + -26x + -9x2 24X + 26xX + 9x2X + 1x3 + x3X = -9 + -26x + -9x2 Add '-1x3' to each side of the equation. 24X + 26xX + 9x2X + 1x3 + -1x3 + x3X = -9 + -26x + -9x2 + -1x3 Combine like terms: 1x3 + -1x3 = 0 24X + 26xX + 9x2X + 0 + x3X = -9 + -26x + -9x2 + -1x3 24X + 26xX + 9x2X + x3X = -9 + -26x + -9x2 + -1x3 Reorder the terms: 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = -9 + -26x + -9x2 + -1x3 + 9 + 26x + 9x2 + x3 Reorder the terms: 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = -9 + 9 + -26x + 26x + -9x2 + 9x2 + -1x3 + x3 Combine like terms: -9 + 9 = 0 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = 0 + -26x + 26x + -9x2 + 9x2 + -1x3 + x3 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = -26x + 26x + -9x2 + 9x2 + -1x3 + x3 Combine like terms: -26x + 26x = 0 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = 0 + -9x2 + 9x2 + -1x3 + x3 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = -9x2 + 9x2 + -1x3 + x3 Combine like terms: -9x2 + 9x2 = 0 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = 0 + -1x3 + x3 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 9 + 24X + 26x + 26xX + 9x2 + 9x2X + x3 + x3X = 0 The solution to this equation could not be determined.
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