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Simplifying (x + 1)(x + 1) = (x + 2)(x + 2) + (x + 3)(x + 3) Reorder the terms: (1 + x)(x + 1) = (x + 2)(x + 2) + (x + 3)(x + 3) Reorder the terms: (1 + x)(1 + x) = (x + 2)(x + 2) + (x + 3)(x + 3) Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) = (x + 2)(x + 2) + (x + 3)(x + 3) ((1 * 1 + x * 1) + x(1 + x)) = (x + 2)(x + 2) + (x + 3)(x + 3) ((1 + 1x) + x(1 + x)) = (x + 2)(x + 2) + (x + 3)(x + 3) (1 + 1x + (1 * x + x * x)) = (x + 2)(x + 2) + (x + 3)(x + 3) (1 + 1x + (1x + x2)) = (x + 2)(x + 2) + (x + 3)(x + 3) Combine like terms: 1x + 1x = 2x (1 + 2x + x2) = (x + 2)(x + 2) + (x + 3)(x + 3) Reorder the terms: 1 + 2x + x2 = (2 + x)(x + 2) + (x + 3)(x + 3) Reorder the terms: 1 + 2x + x2 = (2 + x)(2 + x) + (x + 3)(x + 3) Multiply (2 + x) * (2 + x) 1 + 2x + x2 = (2(2 + x) + x(2 + x)) + (x + 3)(x + 3) 1 + 2x + x2 = ((2 * 2 + x * 2) + x(2 + x)) + (x + 3)(x + 3) 1 + 2x + x2 = ((4 + 2x) + x(2 + x)) + (x + 3)(x + 3) 1 + 2x + x2 = (4 + 2x + (2 * x + x * x)) + (x + 3)(x + 3) 1 + 2x + x2 = (4 + 2x + (2x + x2)) + (x + 3)(x + 3) Combine like terms: 2x + 2x = 4x 1 + 2x + x2 = (4 + 4x + x2) + (x + 3)(x + 3) Reorder the terms: 1 + 2x + x2 = 4 + 4x + x2 + (3 + x)(x + 3) Reorder the terms: 1 + 2x + x2 = 4 + 4x + x2 + (3 + x)(3 + x) Multiply (3 + x) * (3 + x) 1 + 2x + x2 = 4 + 4x + x2 + (3(3 + x) + x(3 + x)) 1 + 2x + x2 = 4 + 4x + x2 + ((3 * 3 + x * 3) + x(3 + x)) 1 + 2x + x2 = 4 + 4x + x2 + ((9 + 3x) + x(3 + x)) 1 + 2x + x2 = 4 + 4x + x2 + (9 + 3x + (3 * x + x * x)) 1 + 2x + x2 = 4 + 4x + x2 + (9 + 3x + (3x + x2)) Combine like terms: 3x + 3x = 6x 1 + 2x + x2 = 4 + 4x + x2 + (9 + 6x + x2) Reorder the terms: 1 + 2x + x2 = 4 + 9 + 4x + 6x + x2 + x2 Combine like terms: 4 + 9 = 13 1 + 2x + x2 = 13 + 4x + 6x + x2 + x2 Combine like terms: 4x + 6x = 10x 1 + 2x + x2 = 13 + 10x + x2 + x2 Combine like terms: x2 + x2 = 2x2 1 + 2x + x2 = 13 + 10x + 2x2 Solving 1 + 2x + x2 = 13 + 10x + 2x2 Solving for variable 'x'. Reorder the terms: 1 + -13 + 2x + -10x + x2 + -2x2 = 13 + 10x + 2x2 + -13 + -10x + -2x2 Combine like terms: 1 + -13 = -12 -12 + 2x + -10x + x2 + -2x2 = 13 + 10x + 2x2 + -13 + -10x + -2x2 Combine like terms: 2x + -10x = -8x -12 + -8x + x2 + -2x2 = 13 + 10x + 2x2 + -13 + -10x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -12 + -8x + -1x2 = 13 + 10x + 2x2 + -13 + -10x + -2x2 Reorder the terms: -12 + -8x + -1x2 = 13 + -13 + 10x + -10x + 2x2 + -2x2 Combine like terms: 13 + -13 = 0 -12 + -8x + -1x2 = 0 + 10x + -10x + 2x2 + -2x2 -12 + -8x + -1x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 -12 + -8x + -1x2 = 0 + 2x2 + -2x2 -12 + -8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8x + x2) = 0 Factor a trinomial. -1((6 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-6, -2}
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