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Simplifying (3d + 1)(d + 4) = 0 Reorder the terms: (1 + 3d)(d + 4) = 0 Reorder the terms: (1 + 3d)(4 + d) = 0 Multiply (1 + 3d) * (4 + d) (1(4 + d) + 3d * (4 + d)) = 0 ((4 * 1 + d * 1) + 3d * (4 + d)) = 0 ((4 + 1d) + 3d * (4 + d)) = 0 (4 + 1d + (4 * 3d + d * 3d)) = 0 (4 + 1d + (12d + 3d2)) = 0 Combine like terms: 1d + 12d = 13d (4 + 13d + 3d2) = 0 Solving 4 + 13d + 3d2 = 0 Solving for variable 'd'. Factor a trinomial. (4 + d)(1 + 3d) = 0Subproblem 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 '(1 + 3d)' equal to zero and attempt to solve: Simplifying 1 + 3d = 0 Solving 1 + 3d = 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 + 3d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3d = 0 + -1 3d = 0 + -1 Combine like terms: 0 + -1 = -1 3d = -1 Divide each side by '3'. d = -0.3333333333 Simplifying d = -0.3333333333Solution
d = {-4, -0.3333333333}
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