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Simplifying (2x + 8)(4x + 6) = 0 Reorder the terms: (8 + 2x)(4x + 6) = 0 Reorder the terms: (8 + 2x)(6 + 4x) = 0 Multiply (8 + 2x) * (6 + 4x) (8(6 + 4x) + 2x * (6 + 4x)) = 0 ((6 * 8 + 4x * 8) + 2x * (6 + 4x)) = 0 ((48 + 32x) + 2x * (6 + 4x)) = 0 (48 + 32x + (6 * 2x + 4x * 2x)) = 0 (48 + 32x + (12x + 8x2)) = 0 Combine like terms: 32x + 12x = 44x (48 + 44x + 8x2) = 0 Solving 48 + 44x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11x + 2x2) = 0 Factor a trinomial. 4((4 + x)(3 + 2x)) = 0 Ignore the factor 4.Subproblem 1
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 = -4Subproblem 2
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 = {-4, -1.5}
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