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Simplifying 9d3 + 6d2 = 24d Reorder the terms: 6d2 + 9d3 = 24d Solving 6d2 + 9d3 = 24d Solving for variable 'd'. Reorder the terms: -24d + 6d2 + 9d3 = 24d + -24d Combine like terms: 24d + -24d = 0 -24d + 6d2 + 9d3 = 0 Factor out the Greatest Common Factor (GCF), '3d'. 3d(-8 + 2d + 3d2) = 0 Factor a trinomial. 3d((-2 + -1d)(4 + -3d)) = 0 Ignore the factor 3.Subproblem 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 '(-2 + -1d)' equal to zero and attempt to solve: Simplifying -2 + -1d = 0 Solving -2 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1d = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1d = 0 + 2 -1d = 0 + 2 Combine like terms: 0 + 2 = 2 -1d = 2 Divide each side by '-1'. d = -2 Simplifying d = -2Subproblem 3
Set the factor '(4 + -3d)' equal to zero and attempt to solve: Simplifying 4 + -3d = 0 Solving 4 + -3d = 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 + -3d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3d = 0 + -4 -3d = 0 + -4 Combine like terms: 0 + -4 = -4 -3d = -4 Divide each side by '-3'. d = 1.333333333 Simplifying d = 1.333333333Solution
d = {0, -2, 1.333333333}
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