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Simplifying (3x + 4)(x + -1)(2x + 1)(4x + -5) = 0 Reorder the terms: (4 + 3x)(x + -1)(2x + 1)(4x + -5) = 0 Reorder the terms: (4 + 3x)(-1 + x)(2x + 1)(4x + -5) = 0 Reorder the terms: (4 + 3x)(-1 + x)(1 + 2x)(4x + -5) = 0 Reorder the terms: (4 + 3x)(-1 + x)(1 + 2x)(-5 + 4x) = 0 Multiply (4 + 3x) * (-1 + x) (4(-1 + x) + 3x * (-1 + x))(1 + 2x)(-5 + 4x) = 0 ((-1 * 4 + x * 4) + 3x * (-1 + x))(1 + 2x)(-5 + 4x) = 0 ((-4 + 4x) + 3x * (-1 + x))(1 + 2x)(-5 + 4x) = 0 (-4 + 4x + (-1 * 3x + x * 3x))(1 + 2x)(-5 + 4x) = 0 (-4 + 4x + (-3x + 3x2))(1 + 2x)(-5 + 4x) = 0 Combine like terms: 4x + -3x = 1x (-4 + 1x + 3x2)(1 + 2x)(-5 + 4x) = 0 Multiply (-4 + 1x + 3x2) * (1 + 2x) (-4(1 + 2x) + 1x * (1 + 2x) + 3x2 * (1 + 2x))(-5 + 4x) = 0 ((1 * -4 + 2x * -4) + 1x * (1 + 2x) + 3x2 * (1 + 2x))(-5 + 4x) = 0 ((-4 + -8x) + 1x * (1 + 2x) + 3x2 * (1 + 2x))(-5 + 4x) = 0 (-4 + -8x + (1 * 1x + 2x * 1x) + 3x2 * (1 + 2x))(-5 + 4x) = 0 (-4 + -8x + (1x + 2x2) + 3x2 * (1 + 2x))(-5 + 4x) = 0 (-4 + -8x + 1x + 2x2 + (1 * 3x2 + 2x * 3x2))(-5 + 4x) = 0 (-4 + -8x + 1x + 2x2 + (3x2 + 6x3))(-5 + 4x) = 0 Combine like terms: -8x + 1x = -7x (-4 + -7x + 2x2 + 3x2 + 6x3)(-5 + 4x) = 0 Combine like terms: 2x2 + 3x2 = 5x2 (-4 + -7x + 5x2 + 6x3)(-5 + 4x) = 0 Multiply (-4 + -7x + 5x2 + 6x3) * (-5 + 4x) (-4(-5 + 4x) + -7x * (-5 + 4x) + 5x2 * (-5 + 4x) + 6x3 * (-5 + 4x)) = 0 ((-5 * -4 + 4x * -4) + -7x * (-5 + 4x) + 5x2 * (-5 + 4x) + 6x3 * (-5 + 4x)) = 0 ((20 + -16x) + -7x * (-5 + 4x) + 5x2 * (-5 + 4x) + 6x3 * (-5 + 4x)) = 0 (20 + -16x + (-5 * -7x + 4x * -7x) + 5x2 * (-5 + 4x) + 6x3 * (-5 + 4x)) = 0 (20 + -16x + (35x + -28x2) + 5x2 * (-5 + 4x) + 6x3 * (-5 + 4x)) = 0 (20 + -16x + 35x + -28x2 + (-5 * 5x2 + 4x * 5x2) + 6x3 * (-5 + 4x)) = 0 (20 + -16x + 35x + -28x2 + (-25x2 + 20x3) + 6x3 * (-5 + 4x)) = 0 (20 + -16x + 35x + -28x2 + -25x2 + 20x3 + (-5 * 6x3 + 4x * 6x3)) = 0 (20 + -16x + 35x + -28x2 + -25x2 + 20x3 + (-30x3 + 24x4)) = 0 Combine like terms: -16x + 35x = 19x (20 + 19x + -28x2 + -25x2 + 20x3 + -30x3 + 24x4) = 0 Combine like terms: -28x2 + -25x2 = -53x2 (20 + 19x + -53x2 + 20x3 + -30x3 + 24x4) = 0 Combine like terms: 20x3 + -30x3 = -10x3 (20 + 19x + -53x2 + -10x3 + 24x4) = 0 Solving 20 + 19x + -53x2 + -10x3 + 24x4 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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