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Simplifying 5d(3 + -1d) + d(2d + -1) = 0 (3 * 5d + -1d * 5d) + d(2d + -1) = 0 (15d + -5d2) + d(2d + -1) = 0 Reorder the terms: 15d + -5d2 + d(-1 + 2d) = 0 15d + -5d2 + (-1 * d + 2d * d) = 0 15d + -5d2 + (-1d + 2d2) = 0 Reorder the terms: 15d + -1d + -5d2 + 2d2 = 0 Combine like terms: 15d + -1d = 14d 14d + -5d2 + 2d2 = 0 Combine like terms: -5d2 + 2d2 = -3d2 14d + -3d2 = 0 Solving 14d + -3d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'd'. d(14 + -3d) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(14 + -3d)' equal to zero and attempt to solve: Simplifying 14 + -3d = 0 Solving 14 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -3d = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -3d = 0 + -14 -3d = 0 + -14 Combine like terms: 0 + -14 = -14 -3d = -14 Divide each side by '-3'. d = 4.666666667 Simplifying d = 4.666666667Solution
d = {0, 4.666666667}
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