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Simplifying 3x(x + 6)(x + 4) = 0 Reorder the terms: 3x(6 + x)(x + 4) = 0 Reorder the terms: 3x(6 + x)(4 + x) = 0 Multiply (6 + x) * (4 + x) 3x(6(4 + x) + x(4 + x)) = 0 3x((4 * 6 + x * 6) + x(4 + x)) = 0 3x((24 + 6x) + x(4 + x)) = 0 3x(24 + 6x + (4 * x + x * x)) = 0 3x(24 + 6x + (4x + x2)) = 0 Combine like terms: 6x + 4x = 10x 3x(24 + 10x + x2) = 0 (24 * 3x + 10x * 3x + x2 * 3x) = 0 (72x + 30x2 + 3x3) = 0 Solving 72x + 30x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(24 + 10x + x2) = 0 Factor a trinomial. 3x((6 + x)(4 + x)) = 0 Ignore the factor 3.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, -6, -4}
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