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Simplifying (5d + 20)(4d + 8) = 0 Reorder the terms: (20 + 5d)(4d + 8) = 0 Reorder the terms: (20 + 5d)(8 + 4d) = 0 Multiply (20 + 5d) * (8 + 4d) (20(8 + 4d) + 5d * (8 + 4d)) = 0 ((8 * 20 + 4d * 20) + 5d * (8 + 4d)) = 0 ((160 + 80d) + 5d * (8 + 4d)) = 0 (160 + 80d + (8 * 5d + 4d * 5d)) = 0 (160 + 80d + (40d + 20d2)) = 0 Combine like terms: 80d + 40d = 120d (160 + 120d + 20d2) = 0 Solving 160 + 120d + 20d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '20'. 20(8 + 6d + d2) = 0 Factor a trinomial. 20((4 + d)(2 + d)) = 0 Ignore the factor 20.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 '(2 + d)' equal to zero and attempt to solve: Simplifying 2 + d = 0 Solving 2 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + d = 0 + -2 Combine like terms: 2 + -2 = 0 0 + d = 0 + -2 d = 0 + -2 Combine like terms: 0 + -2 = -2 d = -2 Simplifying d = -2Solution
d = {-4, -2}
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