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Simplifying (2x + 1)(3x + 1)(4x + -1)(5x + 1) = 0 Reorder the terms: (1 + 2x)(3x + 1)(4x + -1)(5x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 3x)(4x + -1)(5x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 3x)(-1 + 4x)(5x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 3x)(-1 + 4x)(1 + 5x) = 0 Multiply (1 + 2x) * (1 + 3x) (1(1 + 3x) + 2x * (1 + 3x))(-1 + 4x)(1 + 5x) = 0 ((1 * 1 + 3x * 1) + 2x * (1 + 3x))(-1 + 4x)(1 + 5x) = 0 ((1 + 3x) + 2x * (1 + 3x))(-1 + 4x)(1 + 5x) = 0 (1 + 3x + (1 * 2x + 3x * 2x))(-1 + 4x)(1 + 5x) = 0 (1 + 3x + (2x + 6x2))(-1 + 4x)(1 + 5x) = 0 Combine like terms: 3x + 2x = 5x (1 + 5x + 6x2)(-1 + 4x)(1 + 5x) = 0 Multiply (1 + 5x + 6x2) * (-1 + 4x) (1(-1 + 4x) + 5x * (-1 + 4x) + 6x2 * (-1 + 4x))(1 + 5x) = 0 ((-1 * 1 + 4x * 1) + 5x * (-1 + 4x) + 6x2 * (-1 + 4x))(1 + 5x) = 0 ((-1 + 4x) + 5x * (-1 + 4x) + 6x2 * (-1 + 4x))(1 + 5x) = 0 (-1 + 4x + (-1 * 5x + 4x * 5x) + 6x2 * (-1 + 4x))(1 + 5x) = 0 (-1 + 4x + (-5x + 20x2) + 6x2 * (-1 + 4x))(1 + 5x) = 0 (-1 + 4x + -5x + 20x2 + (-1 * 6x2 + 4x * 6x2))(1 + 5x) = 0 (-1 + 4x + -5x + 20x2 + (-6x2 + 24x3))(1 + 5x) = 0 Combine like terms: 4x + -5x = -1x (-1 + -1x + 20x2 + -6x2 + 24x3)(1 + 5x) = 0 Combine like terms: 20x2 + -6x2 = 14x2 (-1 + -1x + 14x2 + 24x3)(1 + 5x) = 0 Multiply (-1 + -1x + 14x2 + 24x3) * (1 + 5x) (-1(1 + 5x) + -1x * (1 + 5x) + 14x2 * (1 + 5x) + 24x3 * (1 + 5x)) = 0 ((1 * -1 + 5x * -1) + -1x * (1 + 5x) + 14x2 * (1 + 5x) + 24x3 * (1 + 5x)) = 0 ((-1 + -5x) + -1x * (1 + 5x) + 14x2 * (1 + 5x) + 24x3 * (1 + 5x)) = 0 (-1 + -5x + (1 * -1x + 5x * -1x) + 14x2 * (1 + 5x) + 24x3 * (1 + 5x)) = 0 (-1 + -5x + (-1x + -5x2) + 14x2 * (1 + 5x) + 24x3 * (1 + 5x)) = 0 (-1 + -5x + -1x + -5x2 + (1 * 14x2 + 5x * 14x2) + 24x3 * (1 + 5x)) = 0 (-1 + -5x + -1x + -5x2 + (14x2 + 70x3) + 24x3 * (1 + 5x)) = 0 (-1 + -5x + -1x + -5x2 + 14x2 + 70x3 + (1 * 24x3 + 5x * 24x3)) = 0 (-1 + -5x + -1x + -5x2 + 14x2 + 70x3 + (24x3 + 120x4)) = 0 Combine like terms: -5x + -1x = -6x (-1 + -6x + -5x2 + 14x2 + 70x3 + 24x3 + 120x4) = 0 Combine like terms: -5x2 + 14x2 = 9x2 (-1 + -6x + 9x2 + 70x3 + 24x3 + 120x4) = 0 Combine like terms: 70x3 + 24x3 = 94x3 (-1 + -6x + 9x2 + 94x3 + 120x4) = 0 Solving -1 + -6x + 9x2 + 94x3 + 120x4 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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