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Simplifying (4x2 + 4x + 1)(x2 + 2x + 1) = x2 + 2x + 1 Reorder the terms: (1 + 4x + 4x2)(x2 + 2x + 1) = x2 + 2x + 1 Reorder the terms: (1 + 4x + 4x2)(1 + 2x + x2) = x2 + 2x + 1 Multiply (1 + 4x + 4x2) * (1 + 2x + x2) (1(1 + 2x + x2) + 4x * (1 + 2x + x2) + 4x2 * (1 + 2x + x2)) = x2 + 2x + 1 ((1 * 1 + 2x * 1 + x2 * 1) + 4x * (1 + 2x + x2) + 4x2 * (1 + 2x + x2)) = x2 + 2x + 1 ((1 + 2x + 1x2) + 4x * (1 + 2x + x2) + 4x2 * (1 + 2x + x2)) = x2 + 2x + 1 (1 + 2x + 1x2 + (1 * 4x + 2x * 4x + x2 * 4x) + 4x2 * (1 + 2x + x2)) = x2 + 2x + 1 (1 + 2x + 1x2 + (4x + 8x2 + 4x3) + 4x2 * (1 + 2x + x2)) = x2 + 2x + 1 (1 + 2x + 1x2 + 4x + 8x2 + 4x3 + (1 * 4x2 + 2x * 4x2 + x2 * 4x2)) = x2 + 2x + 1 (1 + 2x + 1x2 + 4x + 8x2 + 4x3 + (4x2 + 8x3 + 4x4)) = x2 + 2x + 1 Reorder the terms: (1 + 2x + 4x + 1x2 + 8x2 + 4x2 + 4x3 + 8x3 + 4x4) = x2 + 2x + 1 Combine like terms: 2x + 4x = 6x (1 + 6x + 1x2 + 8x2 + 4x2 + 4x3 + 8x3 + 4x4) = x2 + 2x + 1 Combine like terms: 1x2 + 8x2 = 9x2 (1 + 6x + 9x2 + 4x2 + 4x3 + 8x3 + 4x4) = x2 + 2x + 1 Combine like terms: 9x2 + 4x2 = 13x2 (1 + 6x + 13x2 + 4x3 + 8x3 + 4x4) = x2 + 2x + 1 Combine like terms: 4x3 + 8x3 = 12x3 (1 + 6x + 13x2 + 12x3 + 4x4) = x2 + 2x + 1 Reorder the terms: 1 + 6x + 13x2 + 12x3 + 4x4 = 1 + 2x + x2 Add '-1' to each side of the equation. 1 + 6x + 13x2 + 12x3 + -1 + 4x4 = 1 + 2x + -1 + x2 Reorder the terms: 1 + -1 + 6x + 13x2 + 12x3 + 4x4 = 1 + 2x + -1 + x2 Combine like terms: 1 + -1 = 0 0 + 6x + 13x2 + 12x3 + 4x4 = 1 + 2x + -1 + x2 6x + 13x2 + 12x3 + 4x4 = 1 + 2x + -1 + x2 Reorder the terms: 6x + 13x2 + 12x3 + 4x4 = 1 + -1 + 2x + x2 Combine like terms: 1 + -1 = 0 6x + 13x2 + 12x3 + 4x4 = 0 + 2x + x2 6x + 13x2 + 12x3 + 4x4 = 2x + x2 Solving 6x + 13x2 + 12x3 + 4x4 = 2x + x2 Solving for variable 'x'. Reorder the terms: 6x + -2x + 13x2 + -1x2 + 12x3 + 4x4 = 2x + x2 + -2x + -1x2 Combine like terms: 6x + -2x = 4x 4x + 13x2 + -1x2 + 12x3 + 4x4 = 2x + x2 + -2x + -1x2 Combine like terms: 13x2 + -1x2 = 12x2 4x + 12x2 + 12x3 + 4x4 = 2x + x2 + -2x + -1x2 Reorder the terms: 4x + 12x2 + 12x3 + 4x4 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 4x + 12x2 + 12x3 + 4x4 = 0 + x2 + -1x2 4x + 12x2 + 12x3 + 4x4 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4x + 12x2 + 12x3 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(1 + 3x + 3x2 + x3) = 0 Ignore the factor 4.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 + 3x + 3x2 + x3)' equal to zero and attempt to solve: Simplifying 1 + 3x + 3x2 + x3 = 0 Solving 1 + 3x + 3x2 + x3 = 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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