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Simplifying (x + 4)(x + 2)(x + 6) = x2 + 12x2 + 44x + 48 Reorder the terms: (4 + x)(x + 2)(x + 6) = x2 + 12x2 + 44x + 48 Reorder the terms: (4 + x)(2 + x)(x + 6) = x2 + 12x2 + 44x + 48 Reorder the terms: (4 + x)(2 + x)(6 + x) = x2 + 12x2 + 44x + 48 Multiply (4 + x) * (2 + x) (4(2 + x) + x(2 + x))(6 + x) = x2 + 12x2 + 44x + 48 ((2 * 4 + x * 4) + x(2 + x))(6 + x) = x2 + 12x2 + 44x + 48 ((8 + 4x) + x(2 + x))(6 + x) = x2 + 12x2 + 44x + 48 (8 + 4x + (2 * x + x * x))(6 + x) = x2 + 12x2 + 44x + 48 (8 + 4x + (2x + x2))(6 + x) = x2 + 12x2 + 44x + 48 Combine like terms: 4x + 2x = 6x (8 + 6x + x2)(6 + x) = x2 + 12x2 + 44x + 48 Multiply (8 + 6x + x2) * (6 + x) (8(6 + x) + 6x * (6 + x) + x2(6 + x)) = x2 + 12x2 + 44x + 48 ((6 * 8 + x * 8) + 6x * (6 + x) + x2(6 + x)) = x2 + 12x2 + 44x + 48 ((48 + 8x) + 6x * (6 + x) + x2(6 + x)) = x2 + 12x2 + 44x + 48 (48 + 8x + (6 * 6x + x * 6x) + x2(6 + x)) = x2 + 12x2 + 44x + 48 (48 + 8x + (36x + 6x2) + x2(6 + x)) = x2 + 12x2 + 44x + 48 (48 + 8x + 36x + 6x2 + (6 * x2 + x * x2)) = x2 + 12x2 + 44x + 48 (48 + 8x + 36x + 6x2 + (6x2 + x3)) = x2 + 12x2 + 44x + 48 Combine like terms: 8x + 36x = 44x (48 + 44x + 6x2 + 6x2 + x3) = x2 + 12x2 + 44x + 48 Combine like terms: 6x2 + 6x2 = 12x2 (48 + 44x + 12x2 + x3) = x2 + 12x2 + 44x + 48 Reorder the terms: 48 + 44x + 12x2 + x3 = 48 + 44x + x2 + 12x2 Combine like terms: x2 + 12x2 = 13x2 48 + 44x + 12x2 + x3 = 48 + 44x + 13x2 Add '-48' to each side of the equation. 48 + 44x + 12x2 + -48 + x3 = 48 + 44x + -48 + 13x2 Reorder the terms: 48 + -48 + 44x + 12x2 + x3 = 48 + 44x + -48 + 13x2 Combine like terms: 48 + -48 = 0 0 + 44x + 12x2 + x3 = 48 + 44x + -48 + 13x2 44x + 12x2 + x3 = 48 + 44x + -48 + 13x2 Reorder the terms: 44x + 12x2 + x3 = 48 + -48 + 44x + 13x2 Combine like terms: 48 + -48 = 0 44x + 12x2 + x3 = 0 + 44x + 13x2 44x + 12x2 + x3 = 44x + 13x2 Add '-44x' to each side of the equation. 44x + 12x2 + -44x + x3 = 44x + -44x + 13x2 Reorder the terms: 44x + -44x + 12x2 + x3 = 44x + -44x + 13x2 Combine like terms: 44x + -44x = 0 0 + 12x2 + x3 = 44x + -44x + 13x2 12x2 + x3 = 44x + -44x + 13x2 Combine like terms: 44x + -44x = 0 12x2 + x3 = 0 + 13x2 12x2 + x3 = 13x2 Solving 12x2 + x3 = 13x2 Solving for variable 'x'. Reorder the terms: 12x2 + -13x2 + x3 = 13x2 + -13x2 Combine like terms: 12x2 + -13x2 = -1x2 -1x2 + x3 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -1x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + x) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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