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Simplifying (3x + -4) * 2(x + -6) * 4(x + 1)(x + 3) * 6x = 0 Reorder the terms: (-4 + 3x) * 2(x + -6) * 4(x + 1)(x + 3) * 6x = 0 Reorder the terms: (-4 + 3x) * 2(-6 + x) * 4(x + 1)(x + 3) * 6x = 0 Reorder the terms: (-4 + 3x) * 2(-6 + x) * 4(1 + x)(x + 3) * 6x = 0 Reorder the terms: (-4 + 3x) * 2(-6 + x) * 4(1 + x)(3 + x) * 6x = 0 Reorder the terms for easier multiplication: 2 * 4 * 6x(-4 + 3x)(-6 + x)(1 + x)(3 + x) = 0 Multiply 2 * 4 8 * 6x(-4 + 3x)(-6 + x)(1 + x)(3 + x) = 0 Multiply 8 * 6 48x(-4 + 3x)(-6 + x)(1 + x)(3 + x) = 0 Multiply (-4 + 3x) * (-6 + x) 48x(-4(-6 + x) + 3x * (-6 + x))(1 + x)(3 + x) = 0 48x((-6 * -4 + x * -4) + 3x * (-6 + x))(1 + x)(3 + x) = 0 48x((24 + -4x) + 3x * (-6 + x))(1 + x)(3 + x) = 0 48x(24 + -4x + (-6 * 3x + x * 3x))(1 + x)(3 + x) = 0 48x(24 + -4x + (-18x + 3x2))(1 + x)(3 + x) = 0 Combine like terms: -4x + -18x = -22x 48x(24 + -22x + 3x2)(1 + x)(3 + x) = 0 Multiply (24 + -22x + 3x2) * (1 + x) 48x(24(1 + x) + -22x * (1 + x) + 3x2 * (1 + x))(3 + x) = 0 48x((1 * 24 + x * 24) + -22x * (1 + x) + 3x2 * (1 + x))(3 + x) = 0 48x((24 + 24x) + -22x * (1 + x) + 3x2 * (1 + x))(3 + x) = 0 48x(24 + 24x + (1 * -22x + x * -22x) + 3x2 * (1 + x))(3 + x) = 0 48x(24 + 24x + (-22x + -22x2) + 3x2 * (1 + x))(3 + x) = 0 48x(24 + 24x + -22x + -22x2 + (1 * 3x2 + x * 3x2))(3 + x) = 0 48x(24 + 24x + -22x + -22x2 + (3x2 + 3x3))(3 + x) = 0 Combine like terms: 24x + -22x = 2x 48x(24 + 2x + -22x2 + 3x2 + 3x3)(3 + x) = 0 Combine like terms: -22x2 + 3x2 = -19x2 48x(24 + 2x + -19x2 + 3x3)(3 + x) = 0 Multiply (24 + 2x + -19x2 + 3x3) * (3 + x) 48x(24(3 + x) + 2x * (3 + x) + -19x2 * (3 + x) + 3x3 * (3 + x)) = 0 48x((3 * 24 + x * 24) + 2x * (3 + x) + -19x2 * (3 + x) + 3x3 * (3 + x)) = 0 48x((72 + 24x) + 2x * (3 + x) + -19x2 * (3 + x) + 3x3 * (3 + x)) = 0 48x(72 + 24x + (3 * 2x + x * 2x) + -19x2 * (3 + x) + 3x3 * (3 + x)) = 0 48x(72 + 24x + (6x + 2x2) + -19x2 * (3 + x) + 3x3 * (3 + x)) = 0 48x(72 + 24x + 6x + 2x2 + (3 * -19x2 + x * -19x2) + 3x3 * (3 + x)) = 0 48x(72 + 24x + 6x + 2x2 + (-57x2 + -19x3) + 3x3 * (3 + x)) = 0 48x(72 + 24x + 6x + 2x2 + -57x2 + -19x3 + (3 * 3x3 + x * 3x3)) = 0 48x(72 + 24x + 6x + 2x2 + -57x2 + -19x3 + (9x3 + 3x4)) = 0 Combine like terms: 24x + 6x = 30x 48x(72 + 30x + 2x2 + -57x2 + -19x3 + 9x3 + 3x4) = 0 Combine like terms: 2x2 + -57x2 = -55x2 48x(72 + 30x + -55x2 + -19x3 + 9x3 + 3x4) = 0 Combine like terms: -19x3 + 9x3 = -10x3 48x(72 + 30x + -55x2 + -10x3 + 3x4) = 0 (72 * 48x + 30x * 48x + -55x2 * 48x + -10x3 * 48x + 3x4 * 48x) = 0 (3456x + 1440x2 + -2640x3 + -480x4 + 144x5) = 0 Solving 3456x + 1440x2 + -2640x3 + -480x4 + 144x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '48x'. 48x(72 + 30x + -55x2 + -10x3 + 3x4) = 0 Ignore the factor 48.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 '(72 + 30x + -55x2 + -10x3 + 3x4)' equal to zero and attempt to solve: Simplifying 72 + 30x + -55x2 + -10x3 + 3x4 = 0 Solving 72 + 30x + -55x2 + -10x3 + 3x4 = 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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