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Simplifying 6d(d + -1) = 21 + -1d Reorder the terms: 6d(-1 + d) = 21 + -1d (-1 * 6d + d * 6d) = 21 + -1d (-6d + 6d2) = 21 + -1d Solving -6d + 6d2 = 21 + -1d Solving for variable 'd'. Reorder the terms: -21 + -6d + d + 6d2 = 21 + -1d + -21 + d Combine like terms: -6d + d = -5d -21 + -5d + 6d2 = 21 + -1d + -21 + d Reorder the terms: -21 + -5d + 6d2 = 21 + -21 + -1d + d Combine like terms: 21 + -21 = 0 -21 + -5d + 6d2 = 0 + -1d + d -21 + -5d + 6d2 = -1d + d Combine like terms: -1d + d = 0 -21 + -5d + 6d2 = 0 Factor a trinomial. (-3 + -2d)(7 + -3d) = 0Subproblem 1
Set the factor '(-3 + -2d)' equal to zero and attempt to solve: Simplifying -3 + -2d = 0 Solving -3 + -2d = 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 + -2d = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2d = 0 + 3 -2d = 0 + 3 Combine like terms: 0 + 3 = 3 -2d = 3 Divide each side by '-2'. d = -1.5 Simplifying d = -1.5Subproblem 2
Set the factor '(7 + -3d)' equal to zero and attempt to solve: Simplifying 7 + -3d = 0 Solving 7 + -3d = 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 + -3d = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3d = 0 + -7 -3d = 0 + -7 Combine like terms: 0 + -7 = -7 -3d = -7 Divide each side by '-3'. d = 2.333333333 Simplifying d = 2.333333333Solution
d = {-1.5, 2.333333333}
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