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Simplifying (4d + 3)(2d + 7) = 0 Reorder the terms: (3 + 4d)(2d + 7) = 0 Reorder the terms: (3 + 4d)(7 + 2d) = 0 Multiply (3 + 4d) * (7 + 2d) (3(7 + 2d) + 4d * (7 + 2d)) = 0 ((7 * 3 + 2d * 3) + 4d * (7 + 2d)) = 0 ((21 + 6d) + 4d * (7 + 2d)) = 0 (21 + 6d + (7 * 4d + 2d * 4d)) = 0 (21 + 6d + (28d + 8d2)) = 0 Combine like terms: 6d + 28d = 34d (21 + 34d + 8d2) = 0 Solving 21 + 34d + 8d2 = 0 Solving for variable 'd'. Factor a trinomial. (7 + 2d)(3 + 4d) = 0Subproblem 1
Set the factor '(7 + 2d)' equal to zero and attempt to solve: Simplifying 7 + 2d = 0 Solving 7 + 2d = 0 Move all terms containing d to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2d = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2d = 0 + -7 2d = 0 + -7 Combine like terms: 0 + -7 = -7 2d = -7 Divide each side by '2'. d = -3.5 Simplifying d = -3.5Subproblem 2
Set the factor '(3 + 4d)' equal to zero and attempt to solve: Simplifying 3 + 4d = 0 Solving 3 + 4d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4d = 0 + -3 4d = 0 + -3 Combine like terms: 0 + -3 = -3 4d = -3 Divide each side by '4'. d = -0.75 Simplifying d = -0.75Solution
d = {-3.5, -0.75}
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