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Simplifying 2x(x + 2)(x + 6) = 0 Reorder the terms: 2x(2 + x)(x + 6) = 0 Reorder the terms: 2x(2 + x)(6 + x) = 0 Multiply (2 + x) * (6 + x) 2x(2(6 + x) + x(6 + x)) = 0 2x((6 * 2 + x * 2) + x(6 + x)) = 0 2x((12 + 2x) + x(6 + x)) = 0 2x(12 + 2x + (6 * x + x * x)) = 0 2x(12 + 2x + (6x + x2)) = 0 Combine like terms: 2x + 6x = 8x 2x(12 + 8x + x2) = 0 (12 * 2x + 8x * 2x + x2 * 2x) = 0 (24x + 16x2 + 2x3) = 0 Solving 24x + 16x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(12 + 8x + x2) = 0 Factor a trinomial. 2x((6 + x)(2 + x)) = 0 Ignore the factor 2.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 '(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 3
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 = {0, -6, -2}
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