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Simplifying (2x + 4)(4x + 6)(6x + 8x) = 0 Reorder the terms: (4 + 2x)(4x + 6)(6x + 8x) = 0 Reorder the terms: (4 + 2x)(6 + 4x)(6x + 8x) = 0 Combine like terms: 6x + 8x = 14x (4 + 2x)(6 + 4x)(14x) = 0 Remove parenthesis around (14x) (4 + 2x)(6 + 4x) * 14x = 0 Reorder the terms for easier multiplication: 14x(4 + 2x)(6 + 4x) = 0 Multiply (4 + 2x) * (6 + 4x) 14x(4(6 + 4x) + 2x * (6 + 4x)) = 0 14x((6 * 4 + 4x * 4) + 2x * (6 + 4x)) = 0 14x((24 + 16x) + 2x * (6 + 4x)) = 0 14x(24 + 16x + (6 * 2x + 4x * 2x)) = 0 14x(24 + 16x + (12x + 8x2)) = 0 Combine like terms: 16x + 12x = 28x 14x(24 + 28x + 8x2) = 0 (24 * 14x + 28x * 14x + 8x2 * 14x) = 0 (336x + 392x2 + 112x3) = 0 Solving 336x + 392x2 + 112x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '56x'. 56x(6 + 7x + 2x2) = 0 Factor a trinomial. 56x((2 + x)(3 + 2x)) = 0 Ignore the factor 56.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 '(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 = -2Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -2, -1.5}
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