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Simplifying (x + 1)(x + 1)(x + 1) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: (1 + x)(x + 1)(x + 1) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: (1 + x)(1 + x)(x + 1) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: (1 + x)(1 + x)(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x))(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) ((1 * 1 + x * 1) + x(1 + x))(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) ((1 + 1x) + x(1 + x))(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + (1 * x + x * x))(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + (1x + x2))(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 1x + 1x = 2x (1 + 2x + x2)(1 + x) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Multiply (1 + 2x + x2) * (1 + x) (1(1 + x) + 2x * (1 + x) + x2(1 + x)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) ((1 * 1 + x * 1) + 2x * (1 + x) + x2(1 + x)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) ((1 + 1x) + 2x * (1 + x) + x2(1 + x)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + (1 * 2x + x * 2x) + x2(1 + x)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + (2x + 2x2) + x2(1 + x)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + 2x + 2x2 + (1 * x2 + x * x2)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) (1 + 1x + 2x + 2x2 + (1x2 + x3)) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 1x + 2x = 3x (1 + 3x + 2x2 + 1x2 + x3) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 2x2 + 1x2 = 3x2 (1 + 3x + 3x2 + x3) + (x + -2)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: 1 + 3x + 3x2 + x3 + (-2 + x)(x + -2)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: 1 + 3x + 3x2 + x3 + (-2 + x)(-2 + x)(x + -2) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: 1 + 3x + 3x2 + x3 + (-2 + x)(-2 + x)(-2 + x) = (2x + -1)(2x + -1)(2x + -1) Multiply (-2 + x) * (-2 + x) 1 + 3x + 3x2 + x3 + (-2(-2 + x) + x(-2 + x))(-2 + x) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + ((-2 * -2 + x * -2) + x(-2 + x))(-2 + x) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + ((4 + -2x) + x(-2 + x))(-2 + x) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (4 + -2x + (-2 * x + x * x))(-2 + x) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (4 + -2x + (-2x + x2))(-2 + x) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: -2x + -2x = -4x 1 + 3x + 3x2 + x3 + (4 + -4x + x2)(-2 + x) = (2x + -1)(2x + -1)(2x + -1) Multiply (4 + -4x + x2) * (-2 + x) 1 + 3x + 3x2 + x3 + (4(-2 + x) + -4x * (-2 + x) + x2(-2 + x)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + ((-2 * 4 + x * 4) + -4x * (-2 + x) + x2(-2 + x)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + ((-8 + 4x) + -4x * (-2 + x) + x2(-2 + x)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (-8 + 4x + (-2 * -4x + x * -4x) + x2(-2 + x)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (-8 + 4x + (8x + -4x2) + x2(-2 + x)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (-8 + 4x + 8x + -4x2 + (-2 * x2 + x * x2)) = (2x + -1)(2x + -1)(2x + -1) 1 + 3x + 3x2 + x3 + (-8 + 4x + 8x + -4x2 + (-2x2 + x3)) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 4x + 8x = 12x 1 + 3x + 3x2 + x3 + (-8 + 12x + -4x2 + -2x2 + x3) = (2x + -1)(2x + -1)(2x + -1) Combine like terms: -4x2 + -2x2 = -6x2 1 + 3x + 3x2 + x3 + (-8 + 12x + -6x2 + x3) = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: 1 + -8 + 3x + 12x + 3x2 + -6x2 + x3 + x3 = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 1 + -8 = -7 -7 + 3x + 12x + 3x2 + -6x2 + x3 + x3 = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 3x + 12x = 15x -7 + 15x + 3x2 + -6x2 + x3 + x3 = (2x + -1)(2x + -1)(2x + -1) Combine like terms: 3x2 + -6x2 = -3x2 -7 + 15x + -3x2 + x3 + x3 = (2x + -1)(2x + -1)(2x + -1) Combine like terms: x3 + x3 = 2x3 -7 + 15x + -3x2 + 2x3 = (2x + -1)(2x + -1)(2x + -1) Reorder the terms: -7 + 15x + -3x2 + 2x3 = (-1 + 2x)(2x + -1)(2x + -1) Reorder the terms: -7 + 15x + -3x2 + 2x3 = (-1 + 2x)(-1 + 2x)(2x + -1) Reorder the terms: -7 + 15x + -3x2 + 2x3 = (-1 + 2x)(-1 + 2x)(-1 + 2x) Multiply (-1 + 2x) * (-1 + 2x) -7 + 15x + -3x2 + 2x3 = (-1(-1 + 2x) + 2x * (-1 + 2x))(-1 + 2x) -7 + 15x + -3x2 + 2x3 = ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x))(-1 + 2x) -7 + 15x + -3x2 + 2x3 = ((1 + -2x) + 2x * (-1 + 2x))(-1 + 2x) -7 + 15x + -3x2 + 2x3 = (1 + -2x + (-1 * 2x + 2x * 2x))(-1 + 2x) -7 + 15x + -3x2 + 2x3 = (1 + -2x + (-2x + 4x2))(-1 + 2x) Combine like terms: -2x + -2x = -4x -7 + 15x + -3x2 + 2x3 = (1 + -4x + 4x2)(-1 + 2x) Multiply (1 + -4x + 4x2) * (-1 + 2x) -7 + 15x + -3x2 + 2x3 = (1(-1 + 2x) + -4x * (-1 + 2x) + 4x2 * (-1 + 2x)) -7 + 15x + -3x2 + 2x3 = ((-1 * 1 + 2x * 1) + -4x * (-1 + 2x) + 4x2 * (-1 + 2x)) -7 + 15x + -3x2 + 2x3 = ((-1 + 2x) + -4x * (-1 + 2x) + 4x2 * (-1 + 2x)) -7 + 15x + -3x2 + 2x3 = (-1 + 2x + (-1 * -4x + 2x * -4x) + 4x2 * (-1 + 2x)) -7 + 15x + -3x2 + 2x3 = (-1 + 2x + (4x + -8x2) + 4x2 * (-1 + 2x)) -7 + 15x + -3x2 + 2x3 = (-1 + 2x + 4x + -8x2 + (-1 * 4x2 + 2x * 4x2)) -7 + 15x + -3x2 + 2x3 = (-1 + 2x + 4x + -8x2 + (-4x2 + 8x3)) Combine like terms: 2x + 4x = 6x -7 + 15x + -3x2 + 2x3 = (-1 + 6x + -8x2 + -4x2 + 8x3) Combine like terms: -8x2 + -4x2 = -12x2 -7 + 15x + -3x2 + 2x3 = (-1 + 6x + -12x2 + 8x3) Solving -7 + 15x + -3x2 + 2x3 = -1 + 6x + -12x2 + 8x3 Solving for variable 'x'. Reorder the terms: -7 + 1 + 15x + -6x + -3x2 + 12x2 + 2x3 + -8x3 = -1 + 6x + -12x2 + 8x3 + 1 + -6x + 12x2 + -8x3 Combine like terms: -7 + 1 = -6 -6 + 15x + -6x + -3x2 + 12x2 + 2x3 + -8x3 = -1 + 6x + -12x2 + 8x3 + 1 + -6x + 12x2 + -8x3 Combine like terms: 15x + -6x = 9x -6 + 9x + -3x2 + 12x2 + 2x3 + -8x3 = -1 + 6x + -12x2 + 8x3 + 1 + -6x + 12x2 + -8x3 Combine like terms: -3x2 + 12x2 = 9x2 -6 + 9x + 9x2 + 2x3 + -8x3 = -1 + 6x + -12x2 + 8x3 + 1 + -6x + 12x2 + -8x3 Combine like terms: 2x3 + -8x3 = -6x3 -6 + 9x + 9x2 + -6x3 = -1 + 6x + -12x2 + 8x3 + 1 + -6x + 12x2 + -8x3 Reorder the terms: -6 + 9x + 9x2 + -6x3 = -1 + 1 + 6x + -6x + -12x2 + 12x2 + 8x3 + -8x3 Combine like terms: -1 + 1 = 0 -6 + 9x + 9x2 + -6x3 = 0 + 6x + -6x + -12x2 + 12x2 + 8x3 + -8x3 -6 + 9x + 9x2 + -6x3 = 6x + -6x + -12x2 + 12x2 + 8x3 + -8x3 Combine like terms: 6x + -6x = 0 -6 + 9x + 9x2 + -6x3 = 0 + -12x2 + 12x2 + 8x3 + -8x3 -6 + 9x + 9x2 + -6x3 = -12x2 + 12x2 + 8x3 + -8x3 Combine like terms: -12x2 + 12x2 = 0 -6 + 9x + 9x2 + -6x3 = 0 + 8x3 + -8x3 -6 + 9x + 9x2 + -6x3 = 8x3 + -8x3 Combine like terms: 8x3 + -8x3 = 0 -6 + 9x + 9x2 + -6x3 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3x + 3x2 + -2x3) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 3x + 3x2 + -2x3)' equal to zero and attempt to solve: Simplifying -2 + 3x + 3x2 + -2x3 = 0 Solving -2 + 3x + 3x2 + -2x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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