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Simplifying (5x + -4x3 + -7x4)(3x4 + -1x + -18)(4x3 + -30x + 20) = 0 Reorder the terms: (5x + -4x3 + -7x4)(-18 + -1x + 3x4)(4x3 + -30x + 20) = 0 Reorder the terms: (5x + -4x3 + -7x4)(-18 + -1x + 3x4)(20 + -30x + 4x3) = 0 Multiply (5x + -4x3 + -7x4) * (-18 + -1x + 3x4) (5x * (-18 + -1x + 3x4) + -4x3 * (-18 + -1x + 3x4) + -7x4 * (-18 + -1x + 3x4))(20 + -30x + 4x3) = 0 ((-18 * 5x + -1x * 5x + 3x4 * 5x) + -4x3 * (-18 + -1x + 3x4) + -7x4 * (-18 + -1x + 3x4))(20 + -30x + 4x3) = 0 ((-90x + -5x2 + 15x5) + -4x3 * (-18 + -1x + 3x4) + -7x4 * (-18 + -1x + 3x4))(20 + -30x + 4x3) = 0 (-90x + -5x2 + 15x5 + (-18 * -4x3 + -1x * -4x3 + 3x4 * -4x3) + -7x4 * (-18 + -1x + 3x4))(20 + -30x + 4x3) = 0 (-90x + -5x2 + 15x5 + (72x3 + 4x4 + -12x7) + -7x4 * (-18 + -1x + 3x4))(20 + -30x + 4x3) = 0 (-90x + -5x2 + 15x5 + 72x3 + 4x4 + -12x7 + (-18 * -7x4 + -1x * -7x4 + 3x4 * -7x4))(20 + -30x + 4x3) = 0 (-90x + -5x2 + 15x5 + 72x3 + 4x4 + -12x7 + (126x4 + 7x5 + -21x8))(20 + -30x + 4x3) = 0 Reorder the terms: (-90x + -5x2 + 72x3 + 4x4 + 126x4 + 15x5 + 7x5 + -12x7 + -21x8)(20 + -30x + 4x3) = 0 Combine like terms: 4x4 + 126x4 = 130x4 (-90x + -5x2 + 72x3 + 130x4 + 15x5 + 7x5 + -12x7 + -21x8)(20 + -30x + 4x3) = 0 Combine like terms: 15x5 + 7x5 = 22x5 (-90x + -5x2 + 72x3 + 130x4 + 22x5 + -12x7 + -21x8)(20 + -30x + 4x3) = 0 Multiply (-90x + -5x2 + 72x3 + 130x4 + 22x5 + -12x7 + -21x8) * (20 + -30x + 4x3) (-90x * (20 + -30x + 4x3) + -5x2 * (20 + -30x + 4x3) + 72x3 * (20 + -30x + 4x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 ((20 * -90x + -30x * -90x + 4x3 * -90x) + -5x2 * (20 + -30x + 4x3) + 72x3 * (20 + -30x + 4x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 ((-1800x + 2700x2 + -360x4) + -5x2 * (20 + -30x + 4x3) + 72x3 * (20 + -30x + 4x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + (20 * -5x2 + -30x * -5x2 + 4x3 * -5x2) + 72x3 * (20 + -30x + 4x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + (-100x2 + 150x3 + -20x5) + 72x3 * (20 + -30x + 4x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + (20 * 72x3 + -30x * 72x3 + 4x3 * 72x3) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + (1440x3 + -2160x4 + 288x6) + 130x4 * (20 + -30x + 4x3) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + (20 * 130x4 + -30x * 130x4 + 4x3 * 130x4) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + (2600x4 + -3900x5 + 520x7) + 22x5 * (20 + -30x + 4x3) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + (20 * 22x5 + -30x * 22x5 + 4x3 * 22x5) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + (440x5 + -660x6 + 88x8) + -12x7 * (20 + -30x + 4x3) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + 440x5 + -660x6 + 88x8 + (20 * -12x7 + -30x * -12x7 + 4x3 * -12x7) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + 440x5 + -660x6 + 88x8 + (-240x7 + 360x8 + -48x10) + -21x8 * (20 + -30x + 4x3)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + 440x5 + -660x6 + 88x8 + -240x7 + 360x8 + -48x10 + (20 * -21x8 + -30x * -21x8 + 4x3 * -21x8)) = 0 (-1800x + 2700x2 + -360x4 + -100x2 + 150x3 + -20x5 + 1440x3 + -2160x4 + 288x6 + 2600x4 + -3900x5 + 520x7 + 440x5 + -660x6 + 88x8 + -240x7 + 360x8 + -48x10 + (-420x8 + 630x9 + -84x11)) = 0 Reorder the terms: (-1800x + 2700x2 + -100x2 + 150x3 + 1440x3 + -360x4 + -2160x4 + 2600x4 + -20x5 + -3900x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 2700x2 + -100x2 = 2600x2 (-1800x + 2600x2 + 150x3 + 1440x3 + -360x4 + -2160x4 + 2600x4 + -20x5 + -3900x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 150x3 + 1440x3 = 1590x3 (-1800x + 2600x2 + 1590x3 + -360x4 + -2160x4 + 2600x4 + -20x5 + -3900x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: -360x4 + -2160x4 = -2520x4 (-1800x + 2600x2 + 1590x3 + -2520x4 + 2600x4 + -20x5 + -3900x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: -2520x4 + 2600x4 = 80x4 (-1800x + 2600x2 + 1590x3 + 80x4 + -20x5 + -3900x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: -20x5 + -3900x5 = -3920x5 (-1800x + 2600x2 + 1590x3 + 80x4 + -3920x5 + 440x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: -3920x5 + 440x5 = -3480x5 (-1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + 288x6 + -660x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 288x6 + -660x6 = -372x6 (-1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + -372x6 + 520x7 + -240x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 520x7 + -240x7 = 280x7 (-1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + -372x6 + 280x7 + 88x8 + 360x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 88x8 + 360x8 = 448x8 (-1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + -372x6 + 280x7 + 448x8 + -420x8 + 630x9 + -48x10 + -84x11) = 0 Combine like terms: 448x8 + -420x8 = 28x8 (-1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + -372x6 + 280x7 + 28x8 + 630x9 + -48x10 + -84x11) = 0 Solving -1800x + 2600x2 + 1590x3 + 80x4 + -3480x5 + -372x6 + 280x7 + 28x8 + 630x9 + -48x10 + -84x11 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-900 + 1300x + 795x2 + 40x3 + -1740x4 + -186x5 + 140x6 + 14x7 + 315x8 + -24x9 + -42x10) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-900 + 1300x + 795x2 + 40x3 + -1740x4 + -186x5 + 140x6 + 14x7 + 315x8 + -24x9 + -42x10)' equal to zero and attempt to solve: Simplifying -900 + 1300x + 795x2 + 40x3 + -1740x4 + -186x5 + 140x6 + 14x7 + 315x8 + -24x9 + -42x10 = 0 Solving -900 + 1300x + 795x2 + 40x3 + -1740x4 + -186x5 + 140x6 + 14x7 + 315x8 + -24x9 + -42x10 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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