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Simplifying 4d(3d + -2) = 8d + -5 Reorder the terms: 4d(-2 + 3d) = 8d + -5 (-2 * 4d + 3d * 4d) = 8d + -5 (-8d + 12d2) = 8d + -5 Reorder the terms: -8d + 12d2 = -5 + 8d Solving -8d + 12d2 = -5 + 8d Solving for variable 'd'. Reorder the terms: 5 + -8d + -8d + 12d2 = -5 + 8d + 5 + -8d Combine like terms: -8d + -8d = -16d 5 + -16d + 12d2 = -5 + 8d + 5 + -8d Reorder the terms: 5 + -16d + 12d2 = -5 + 5 + 8d + -8d Combine like terms: -5 + 5 = 0 5 + -16d + 12d2 = 0 + 8d + -8d 5 + -16d + 12d2 = 8d + -8d Combine like terms: 8d + -8d = 0 5 + -16d + 12d2 = 0 Factor a trinomial. (1 + -2d)(5 + -6d) = 0Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(5 + -6d)' equal to zero and attempt to solve: Simplifying 5 + -6d = 0 Solving 5 + -6d = 0 Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6d = 0 + -5 -6d = 0 + -5 Combine like terms: 0 + -5 = -5 -6d = -5 Divide each side by '-6'. d = 0.8333333333 Simplifying d = 0.8333333333Solution
d = {0.5, 0.8333333333}
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