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Simplifying (2x + 1)(2x + 1)(x + 1)(8x + 1)(7x + 1) = 0 Reorder the terms: (1 + 2x)(2x + 1)(x + 1)(8x + 1)(7x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 2x)(x + 1)(8x + 1)(7x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 2x)(1 + x)(8x + 1)(7x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 2x)(1 + x)(1 + 8x)(7x + 1) = 0 Reorder the terms: (1 + 2x)(1 + 2x)(1 + x)(1 + 8x)(1 + 7x) = 0 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x))(1 + x)(1 + 8x)(1 + 7x) = 0 ((1 * 1 + 2x * 1) + 2x * (1 + 2x))(1 + x)(1 + 8x)(1 + 7x) = 0 ((1 + 2x) + 2x * (1 + 2x))(1 + x)(1 + 8x)(1 + 7x) = 0 (1 + 2x + (1 * 2x + 2x * 2x))(1 + x)(1 + 8x)(1 + 7x) = 0 (1 + 2x + (2x + 4x2))(1 + x)(1 + 8x)(1 + 7x) = 0 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2)(1 + x)(1 + 8x)(1 + 7x) = 0 Multiply (1 + 4x + 4x2) * (1 + x) (1(1 + x) + 4x * (1 + x) + 4x2 * (1 + x))(1 + 8x)(1 + 7x) = 0 ((1 * 1 + x * 1) + 4x * (1 + x) + 4x2 * (1 + x))(1 + 8x)(1 + 7x) = 0 ((1 + 1x) + 4x * (1 + x) + 4x2 * (1 + x))(1 + 8x)(1 + 7x) = 0 (1 + 1x + (1 * 4x + x * 4x) + 4x2 * (1 + x))(1 + 8x)(1 + 7x) = 0 (1 + 1x + (4x + 4x2) + 4x2 * (1 + x))(1 + 8x)(1 + 7x) = 0 (1 + 1x + 4x + 4x2 + (1 * 4x2 + x * 4x2))(1 + 8x)(1 + 7x) = 0 (1 + 1x + 4x + 4x2 + (4x2 + 4x3))(1 + 8x)(1 + 7x) = 0 Combine like terms: 1x + 4x = 5x (1 + 5x + 4x2 + 4x2 + 4x3)(1 + 8x)(1 + 7x) = 0 Combine like terms: 4x2 + 4x2 = 8x2 (1 + 5x + 8x2 + 4x3)(1 + 8x)(1 + 7x) = 0 Multiply (1 + 5x + 8x2 + 4x3) * (1 + 8x) (1(1 + 8x) + 5x * (1 + 8x) + 8x2 * (1 + 8x) + 4x3 * (1 + 8x))(1 + 7x) = 0 ((1 * 1 + 8x * 1) + 5x * (1 + 8x) + 8x2 * (1 + 8x) + 4x3 * (1 + 8x))(1 + 7x) = 0 ((1 + 8x) + 5x * (1 + 8x) + 8x2 * (1 + 8x) + 4x3 * (1 + 8x))(1 + 7x) = 0 (1 + 8x + (1 * 5x + 8x * 5x) + 8x2 * (1 + 8x) + 4x3 * (1 + 8x))(1 + 7x) = 0 (1 + 8x + (5x + 40x2) + 8x2 * (1 + 8x) + 4x3 * (1 + 8x))(1 + 7x) = 0 (1 + 8x + 5x + 40x2 + (1 * 8x2 + 8x * 8x2) + 4x3 * (1 + 8x))(1 + 7x) = 0 (1 + 8x + 5x + 40x2 + (8x2 + 64x3) + 4x3 * (1 + 8x))(1 + 7x) = 0 (1 + 8x + 5x + 40x2 + 8x2 + 64x3 + (1 * 4x3 + 8x * 4x3))(1 + 7x) = 0 (1 + 8x + 5x + 40x2 + 8x2 + 64x3 + (4x3 + 32x4))(1 + 7x) = 0 Combine like terms: 8x + 5x = 13x (1 + 13x + 40x2 + 8x2 + 64x3 + 4x3 + 32x4)(1 + 7x) = 0 Combine like terms: 40x2 + 8x2 = 48x2 (1 + 13x + 48x2 + 64x3 + 4x3 + 32x4)(1 + 7x) = 0 Combine like terms: 64x3 + 4x3 = 68x3 (1 + 13x + 48x2 + 68x3 + 32x4)(1 + 7x) = 0 Multiply (1 + 13x + 48x2 + 68x3 + 32x4) * (1 + 7x) (1(1 + 7x) + 13x * (1 + 7x) + 48x2 * (1 + 7x) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 ((1 * 1 + 7x * 1) + 13x * (1 + 7x) + 48x2 * (1 + 7x) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 ((1 + 7x) + 13x * (1 + 7x) + 48x2 * (1 + 7x) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 (1 + 7x + (1 * 13x + 7x * 13x) + 48x2 * (1 + 7x) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 (1 + 7x + (13x + 91x2) + 48x2 * (1 + 7x) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 (1 + 7x + 13x + 91x2 + (1 * 48x2 + 7x * 48x2) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 (1 + 7x + 13x + 91x2 + (48x2 + 336x3) + 68x3 * (1 + 7x) + 32x4 * (1 + 7x)) = 0 (1 + 7x + 13x + 91x2 + 48x2 + 336x3 + (1 * 68x3 + 7x * 68x3) + 32x4 * (1 + 7x)) = 0 (1 + 7x + 13x + 91x2 + 48x2 + 336x3 + (68x3 + 476x4) + 32x4 * (1 + 7x)) = 0 (1 + 7x + 13x + 91x2 + 48x2 + 336x3 + 68x3 + 476x4 + (1 * 32x4 + 7x * 32x4)) = 0 (1 + 7x + 13x + 91x2 + 48x2 + 336x3 + 68x3 + 476x4 + (32x4 + 224x5)) = 0 Combine like terms: 7x + 13x = 20x (1 + 20x + 91x2 + 48x2 + 336x3 + 68x3 + 476x4 + 32x4 + 224x5) = 0 Combine like terms: 91x2 + 48x2 = 139x2 (1 + 20x + 139x2 + 336x3 + 68x3 + 476x4 + 32x4 + 224x5) = 0 Combine like terms: 336x3 + 68x3 = 404x3 (1 + 20x + 139x2 + 404x3 + 476x4 + 32x4 + 224x5) = 0 Combine like terms: 476x4 + 32x4 = 508x4 (1 + 20x + 139x2 + 404x3 + 508x4 + 224x5) = 0 Solving 1 + 20x + 139x2 + 404x3 + 508x4 + 224x5 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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