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Simplifying (2d + 8)(3d + 12) = 0 Reorder the terms: (8 + 2d)(3d + 12) = 0 Reorder the terms: (8 + 2d)(12 + 3d) = 0 Multiply (8 + 2d) * (12 + 3d) (8(12 + 3d) + 2d * (12 + 3d)) = 0 ((12 * 8 + 3d * 8) + 2d * (12 + 3d)) = 0 ((96 + 24d) + 2d * (12 + 3d)) = 0 (96 + 24d + (12 * 2d + 3d * 2d)) = 0 (96 + 24d + (24d + 6d2)) = 0 Combine like terms: 24d + 24d = 48d (96 + 48d + 6d2) = 0 Solving 96 + 48d + 6d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '6'. 6(16 + 8d + d2) = 0 Factor a trinomial. 6((4 + d)(4 + d)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + d)' equal to zero and attempt to solve: Simplifying 4 + d = 0 Solving 4 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + d = 0 + -4 d = 0 + -4 Combine like terms: 0 + -4 = -4 d = -4 Simplifying d = -4Subproblem 2
Set the factor '(4 + d)' equal to zero and attempt to solve: Simplifying 4 + d = 0 Solving 4 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + d = 0 + -4 d = 0 + -4 Combine like terms: 0 + -4 = -4 d = -4 Simplifying d = -4Solution
d = {-4, -4}
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