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Simplifying (X + 1)(2 + -1x)(3x + -1)(4x + 1)(1 + -5x) = 0 Reorder the terms: (1 + X)(2 + -1x)(3x + -1)(4x + 1)(1 + -5x) = 0 Reorder the terms: (1 + X)(2 + -1x)(-1 + 3x)(4x + 1)(1 + -5x) = 0 Reorder the terms: (1 + X)(2 + -1x)(-1 + 3x)(1 + 4x)(1 + -5x) = 0 Multiply (1 + X) * (2 + -1x) (1(2 + -1x) + X(2 + -1x))(-1 + 3x)(1 + 4x)(1 + -5x) = 0 ((2 * 1 + -1x * 1) + X(2 + -1x))(-1 + 3x)(1 + 4x)(1 + -5x) = 0 ((2 + -1x) + X(2 + -1x))(-1 + 3x)(1 + 4x)(1 + -5x) = 0 (2 + -1x + (2 * X + -1x * X))(-1 + 3x)(1 + 4x)(1 + -5x) = 0 (2 + -1x + (2X + -1xX))(-1 + 3x)(1 + 4x)(1 + -5x) = 0 Reorder the terms: (2 + 2X + -1x + -1xX)(-1 + 3x)(1 + 4x)(1 + -5x) = 0 (2 + 2X + -1x + -1xX)(-1 + 3x)(1 + 4x)(1 + -5x) = 0 Multiply (2 + 2X + -1x + -1xX) * (-1 + 3x) (2(-1 + 3x) + 2X * (-1 + 3x) + -1x * (-1 + 3x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 ((-1 * 2 + 3x * 2) + 2X * (-1 + 3x) + -1x * (-1 + 3x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 ((-2 + 6x) + 2X * (-1 + 3x) + -1x * (-1 + 3x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + (-1 * 2X + 3x * 2X) + -1x * (-1 + 3x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + (-2X + 6xX) + -1x * (-1 + 3x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + -2X + 6xX + (-1 * -1x + 3x * -1x) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + -2X + 6xX + (1x + -3x2) + -1xX * (-1 + 3x))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + -2X + 6xX + 1x + -3x2 + (-1 * -1xX + 3x * -1xX))(1 + 4x)(1 + -5x) = 0 (-2 + 6x + -2X + 6xX + 1x + -3x2 + (1xX + -3x2X))(1 + 4x)(1 + -5x) = 0 Reorder the terms: (-2 + -2X + 6x + 1x + 6xX + 1xX + -3x2 + -3x2X)(1 + 4x)(1 + -5x) = 0 Combine like terms: 6x + 1x = 7x (-2 + -2X + 7x + 6xX + 1xX + -3x2 + -3x2X)(1 + 4x)(1 + -5x) = 0 Combine like terms: 6xX + 1xX = 7xX (-2 + -2X + 7x + 7xX + -3x2 + -3x2X)(1 + 4x)(1 + -5x) = 0 Multiply (-2 + -2X + 7x + 7xX + -3x2 + -3x2X) * (1 + 4x) (-2(1 + 4x) + -2X * (1 + 4x) + 7x * (1 + 4x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 ((1 * -2 + 4x * -2) + -2X * (1 + 4x) + 7x * (1 + 4x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 ((-2 + -8x) + -2X * (1 + 4x) + 7x * (1 + 4x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + (1 * -2X + 4x * -2X) + 7x * (1 + 4x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + (-2X + -8xX) + 7x * (1 + 4x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + (1 * 7x + 4x * 7x) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + (7x + 28x2) + 7xX * (1 + 4x) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + (1 * 7xX + 4x * 7xX) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + (7xX + 28x2X) + -3x2 * (1 + 4x) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + 7xX + 28x2X + (1 * -3x2 + 4x * -3x2) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + 7xX + 28x2X + (-3x2 + -12x3) + -3x2X * (1 + 4x))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + 7xX + 28x2X + -3x2 + -12x3 + (1 * -3x2X + 4x * -3x2X))(1 + -5x) = 0 (-2 + -8x + -2X + -8xX + 7x + 28x2 + 7xX + 28x2X + -3x2 + -12x3 + (-3x2X + -12x3X))(1 + -5x) = 0 Reorder the terms: (-2 + -2X + -8x + 7x + -8xX + 7xX + 28x2 + -3x2 + 28x2X + -3x2X + -12x3 + -12x3X)(1 + -5x) = 0 Combine like terms: -8x + 7x = -1x (-2 + -2X + -1x + -8xX + 7xX + 28x2 + -3x2 + 28x2X + -3x2X + -12x3 + -12x3X)(1 + -5x) = 0 Combine like terms: -8xX + 7xX = -1xX (-2 + -2X + -1x + -1xX + 28x2 + -3x2 + 28x2X + -3x2X + -12x3 + -12x3X)(1 + -5x) = 0 Combine like terms: 28x2 + -3x2 = 25x2 (-2 + -2X + -1x + -1xX + 25x2 + 28x2X + -3x2X + -12x3 + -12x3X)(1 + -5x) = 0 Combine like terms: 28x2X + -3x2X = 25x2X (-2 + -2X + -1x + -1xX + 25x2 + 25x2X + -12x3 + -12x3X)(1 + -5x) = 0 Multiply (-2 + -2X + -1x + -1xX + 25x2 + 25x2X + -12x3 + -12x3X) * (1 + -5x) (-2(1 + -5x) + -2X * (1 + -5x) + -1x * (1 + -5x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 ((1 * -2 + -5x * -2) + -2X * (1 + -5x) + -1x * (1 + -5x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 ((-2 + 10x) + -2X * (1 + -5x) + -1x * (1 + -5x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + (1 * -2X + -5x * -2X) + -1x * (1 + -5x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + (-2X + 10xX) + -1x * (1 + -5x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + (1 * -1x + -5x * -1x) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + (-1x + 5x2) + -1xX * (1 + -5x) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + (1 * -1xX + -5x * -1xX) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + (-1xX + 5x2X) + 25x2 * (1 + -5x) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + (1 * 25x2 + -5x * 25x2) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + (25x2 + -125x3) + 25x2X * (1 + -5x) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + (1 * 25x2X + -5x * 25x2X) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + (25x2X + -125x3X) + -12x3 * (1 + -5x) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + 25x2X + -125x3X + (1 * -12x3 + -5x * -12x3) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + 25x2X + -125x3X + (-12x3 + 60x4) + -12x3X * (1 + -5x)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + 25x2X + -125x3X + -12x3 + 60x4 + (1 * -12x3X + -5x * -12x3X)) = 0 (-2 + 10x + -2X + 10xX + -1x + 5x2 + -1xX + 5x2X + 25x2 + -125x3 + 25x2X + -125x3X + -12x3 + 60x4 + (-12x3X + 60x4X)) = 0 Reorder the terms: (-2 + -2X + 10x + -1x + 10xX + -1xX + 5x2 + 25x2 + 5x2X + 25x2X + -125x3 + -12x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: 10x + -1x = 9x (-2 + -2X + 9x + 10xX + -1xX + 5x2 + 25x2 + 5x2X + 25x2X + -125x3 + -12x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: 10xX + -1xX = 9xX (-2 + -2X + 9x + 9xX + 5x2 + 25x2 + 5x2X + 25x2X + -125x3 + -12x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: 5x2 + 25x2 = 30x2 (-2 + -2X + 9x + 9xX + 30x2 + 5x2X + 25x2X + -125x3 + -12x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: 5x2X + 25x2X = 30x2X (-2 + -2X + 9x + 9xX + 30x2 + 30x2X + -125x3 + -12x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: -125x3 + -12x3 = -137x3 (-2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -125x3X + -12x3X + 60x4 + 60x4X) = 0 Combine like terms: -125x3X + -12x3X = -137x3X (-2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X) = 0 Solving -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 2 + 60x4X = 0 + 2 Reorder the terms: -2 + 2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + 2 -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + 2 Combine like terms: 0 + 2 = 2 -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 Add '-9x' to each side of the equation. -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + -9x + 60x4X = 2 + -9x Reorder the terms: -2X + 9x + -9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x Combine like terms: 9x + -9x = 0 -2X + 0 + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x -2X + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x Add '-30x2' to each side of the equation. -2X + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + -30x2 + 60x4X = 2 + -9x + -30x2 Reorder the terms: -2X + 9xX + 30x2 + -30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 Combine like terms: 30x2 + -30x2 = 0 -2X + 9xX + 0 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 -2X + 9xX + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 Add '137x3' to each side of the equation. -2X + 9xX + 30x2X + -137x3 + -137x3X + 60x4 + 137x3 + 60x4X = 2 + -9x + -30x2 + 137x3 Reorder the terms: -2X + 9xX + 30x2X + -137x3 + 137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 + 137x3 Combine like terms: -137x3 + 137x3 = 0 -2X + 9xX + 30x2X + 0 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 + 137x3 -2X + 9xX + 30x2X + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 + 137x3 Add '-60x4' to each side of the equation. -2X + 9xX + 30x2X + -137x3X + 60x4 + -60x4 + 60x4X = 2 + -9x + -30x2 + 137x3 + -60x4 Combine like terms: 60x4 + -60x4 = 0 -2X + 9xX + 30x2X + -137x3X + 0 + 60x4X = 2 + -9x + -30x2 + 137x3 + -60x4 -2X + 9xX + 30x2X + -137x3X + 60x4X = 2 + -9x + -30x2 + 137x3 + -60x4 Reorder the terms: -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -9x + -30x2 + 137x3 + -60x4 + -2 + 9x + 30x2 + -137x3 + 60x4 Reorder the terms: -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 2 + -2 + -9x + 9x + -30x2 + 30x2 + 137x3 + -137x3 + -60x4 + 60x4 Combine like terms: 2 + -2 = 0 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + -9x + 9x + -30x2 + 30x2 + 137x3 + -137x3 + -60x4 + 60x4 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = -9x + 9x + -30x2 + 30x2 + 137x3 + -137x3 + -60x4 + 60x4 Combine like terms: -9x + 9x = 0 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + -30x2 + 30x2 + 137x3 + -137x3 + -60x4 + 60x4 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = -30x2 + 30x2 + 137x3 + -137x3 + -60x4 + 60x4 Combine like terms: -30x2 + 30x2 = 0 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + 137x3 + -137x3 + -60x4 + 60x4 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 137x3 + -137x3 + -60x4 + 60x4 Combine like terms: 137x3 + -137x3 = 0 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 + -60x4 + 60x4 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = -60x4 + 60x4 Combine like terms: -60x4 + 60x4 = 0 -2 + -2X + 9x + 9xX + 30x2 + 30x2X + -137x3 + -137x3X + 60x4 + 60x4X = 0 The solution to this equation could not be determined.
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