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Simplifying (2x + 1)(3x + 1)(4x + 1)(5x + 1)(6x + 1) * 7x = 0 Reorder the terms: (1 + 2x)(3x + 1)(4x + 1)(5x + 1)(6x + 1) * 7x = 0 Reorder the terms: (1 + 2x)(1 + 3x)(4x + 1)(5x + 1)(6x + 1) * 7x = 0 Reorder the terms: (1 + 2x)(1 + 3x)(1 + 4x)(5x + 1)(6x + 1) * 7x = 0 Reorder the terms: (1 + 2x)(1 + 3x)(1 + 4x)(1 + 5x)(6x + 1) * 7x = 0 Reorder the terms: (1 + 2x)(1 + 3x)(1 + 4x)(1 + 5x)(1 + 6x) * 7x = 0 Reorder the terms for easier multiplication: 7x(1 + 2x)(1 + 3x)(1 + 4x)(1 + 5x)(1 + 6x) = 0 Multiply (1 + 2x) * (1 + 3x) 7x(1(1 + 3x) + 2x * (1 + 3x))(1 + 4x)(1 + 5x)(1 + 6x) = 0 7x((1 * 1 + 3x * 1) + 2x * (1 + 3x))(1 + 4x)(1 + 5x)(1 + 6x) = 0 7x((1 + 3x) + 2x * (1 + 3x))(1 + 4x)(1 + 5x)(1 + 6x) = 0 7x(1 + 3x + (1 * 2x + 3x * 2x))(1 + 4x)(1 + 5x)(1 + 6x) = 0 7x(1 + 3x + (2x + 6x2))(1 + 4x)(1 + 5x)(1 + 6x) = 0 Combine like terms: 3x + 2x = 5x 7x(1 + 5x + 6x2)(1 + 4x)(1 + 5x)(1 + 6x) = 0 Multiply (1 + 5x + 6x2) * (1 + 4x) 7x(1(1 + 4x) + 5x * (1 + 4x) + 6x2 * (1 + 4x))(1 + 5x)(1 + 6x) = 0 7x((1 * 1 + 4x * 1) + 5x * (1 + 4x) + 6x2 * (1 + 4x))(1 + 5x)(1 + 6x) = 0 7x((1 + 4x) + 5x * (1 + 4x) + 6x2 * (1 + 4x))(1 + 5x)(1 + 6x) = 0 7x(1 + 4x + (1 * 5x + 4x * 5x) + 6x2 * (1 + 4x))(1 + 5x)(1 + 6x) = 0 7x(1 + 4x + (5x + 20x2) + 6x2 * (1 + 4x))(1 + 5x)(1 + 6x) = 0 7x(1 + 4x + 5x + 20x2 + (1 * 6x2 + 4x * 6x2))(1 + 5x)(1 + 6x) = 0 7x(1 + 4x + 5x + 20x2 + (6x2 + 24x3))(1 + 5x)(1 + 6x) = 0 Combine like terms: 4x + 5x = 9x 7x(1 + 9x + 20x2 + 6x2 + 24x3)(1 + 5x)(1 + 6x) = 0 Combine like terms: 20x2 + 6x2 = 26x2 7x(1 + 9x + 26x2 + 24x3)(1 + 5x)(1 + 6x) = 0 Multiply (1 + 9x + 26x2 + 24x3) * (1 + 5x) 7x(1(1 + 5x) + 9x * (1 + 5x) + 26x2 * (1 + 5x) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x((1 * 1 + 5x * 1) + 9x * (1 + 5x) + 26x2 * (1 + 5x) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x((1 + 5x) + 9x * (1 + 5x) + 26x2 * (1 + 5x) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x(1 + 5x + (1 * 9x + 5x * 9x) + 26x2 * (1 + 5x) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x(1 + 5x + (9x + 45x2) + 26x2 * (1 + 5x) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x(1 + 5x + 9x + 45x2 + (1 * 26x2 + 5x * 26x2) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x(1 + 5x + 9x + 45x2 + (26x2 + 130x3) + 24x3 * (1 + 5x))(1 + 6x) = 0 7x(1 + 5x + 9x + 45x2 + 26x2 + 130x3 + (1 * 24x3 + 5x * 24x3))(1 + 6x) = 0 7x(1 + 5x + 9x + 45x2 + 26x2 + 130x3 + (24x3 + 120x4))(1 + 6x) = 0 Combine like terms: 5x + 9x = 14x 7x(1 + 14x + 45x2 + 26x2 + 130x3 + 24x3 + 120x4)(1 + 6x) = 0 Combine like terms: 45x2 + 26x2 = 71x2 7x(1 + 14x + 71x2 + 130x3 + 24x3 + 120x4)(1 + 6x) = 0 Combine like terms: 130x3 + 24x3 = 154x3 7x(1 + 14x + 71x2 + 154x3 + 120x4)(1 + 6x) = 0 Multiply (1 + 14x + 71x2 + 154x3 + 120x4) * (1 + 6x) 7x(1(1 + 6x) + 14x * (1 + 6x) + 71x2 * (1 + 6x) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x((1 * 1 + 6x * 1) + 14x * (1 + 6x) + 71x2 * (1 + 6x) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x((1 + 6x) + 14x * (1 + 6x) + 71x2 * (1 + 6x) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + (1 * 14x + 6x * 14x) + 71x2 * (1 + 6x) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + (14x + 84x2) + 71x2 * (1 + 6x) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + 14x + 84x2 + (1 * 71x2 + 6x * 71x2) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + 14x + 84x2 + (71x2 + 426x3) + 154x3 * (1 + 6x) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + 14x + 84x2 + 71x2 + 426x3 + (1 * 154x3 + 6x * 154x3) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + 14x + 84x2 + 71x2 + 426x3 + (154x3 + 924x4) + 120x4 * (1 + 6x)) = 0 7x(1 + 6x + 14x + 84x2 + 71x2 + 426x3 + 154x3 + 924x4 + (1 * 120x4 + 6x * 120x4)) = 0 7x(1 + 6x + 14x + 84x2 + 71x2 + 426x3 + 154x3 + 924x4 + (120x4 + 720x5)) = 0 Combine like terms: 6x + 14x = 20x 7x(1 + 20x + 84x2 + 71x2 + 426x3 + 154x3 + 924x4 + 120x4 + 720x5) = 0 Combine like terms: 84x2 + 71x2 = 155x2 7x(1 + 20x + 155x2 + 426x3 + 154x3 + 924x4 + 120x4 + 720x5) = 0 Combine like terms: 426x3 + 154x3 = 580x3 7x(1 + 20x + 155x2 + 580x3 + 924x4 + 120x4 + 720x5) = 0 Combine like terms: 924x4 + 120x4 = 1044x4 7x(1 + 20x + 155x2 + 580x3 + 1044x4 + 720x5) = 0 (1 * 7x + 20x * 7x + 155x2 * 7x + 580x3 * 7x + 1044x4 * 7x + 720x5 * 7x) = 0 (7x + 140x2 + 1085x3 + 4060x4 + 7308x5 + 5040x6) = 0 Solving 7x + 140x2 + 1085x3 + 4060x4 + 7308x5 + 5040x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x'. 7x(1 + 20x + 155x2 + 580x3 + 1044x4 + 720x5) = 0 Ignore the factor 7.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 '(1 + 20x + 155x2 + 580x3 + 1044x4 + 720x5)' equal to zero and attempt to solve: Simplifying 1 + 20x + 155x2 + 580x3 + 1044x4 + 720x5 = 0 Solving 1 + 20x + 155x2 + 580x3 + 1044x4 + 720x5 = 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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