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Simplifying (2d + 1)(d + 8) = 0 Reorder the terms: (1 + 2d)(d + 8) = 0 Reorder the terms: (1 + 2d)(8 + d) = 0 Multiply (1 + 2d) * (8 + d) (1(8 + d) + 2d * (8 + d)) = 0 ((8 * 1 + d * 1) + 2d * (8 + d)) = 0 ((8 + 1d) + 2d * (8 + d)) = 0 (8 + 1d + (8 * 2d + d * 2d)) = 0 (8 + 1d + (16d + 2d2)) = 0 Combine like terms: 1d + 16d = 17d (8 + 17d + 2d2) = 0 Solving 8 + 17d + 2d2 = 0 Solving for variable 'd'. Factor a trinomial. (8 + d)(1 + 2d) = 0Subproblem 1
Set the factor '(8 + d)' equal to zero and attempt to solve: Simplifying 8 + d = 0 Solving 8 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + d = 0 + -8 Combine like terms: 8 + -8 = 0 0 + d = 0 + -8 d = 0 + -8 Combine like terms: 0 + -8 = -8 d = -8 Simplifying d = -8Subproblem 2
Set the factor '(1 + 2d)' equal to zero and attempt to solve: Simplifying 1 + 2d = 0 Solving 1 + 2d = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2d = 0 + -1 2d = 0 + -1 Combine like terms: 0 + -1 = -1 2d = -1 Divide each side by '2'. d = -0.5 Simplifying d = -0.5Solution
d = {-8, -0.5}
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