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Simplifying 5d3 + -40d2 = -75d Reorder the terms: -40d2 + 5d3 = -75d Solving -40d2 + 5d3 = -75d Solving for variable 'd'. Reorder the terms: 75d + -40d2 + 5d3 = -75d + 75d Combine like terms: -75d + 75d = 0 75d + -40d2 + 5d3 = 0 Factor out the Greatest Common Factor (GCF), '5d'. 5d(15 + -8d + d2) = 0 Factor a trinomial. 5d((3 + -1d)(5 + -1d)) = 0 Ignore the factor 5.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 '(3 + -1d)' equal to zero and attempt to solve: Simplifying 3 + -1d = 0 Solving 3 + -1d = 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 + -1d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d = 0 + -3 -1d = 0 + -3 Combine like terms: 0 + -3 = -3 -1d = -3 Divide each side by '-1'. d = 3 Simplifying d = 3Subproblem 3
Set the factor '(5 + -1d)' equal to zero and attempt to solve: Simplifying 5 + -1d = 0 Solving 5 + -1d = 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 + -1d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1d = 0 + -5 -1d = 0 + -5 Combine like terms: 0 + -5 = -5 -1d = -5 Divide each side by '-1'. d = 5 Simplifying d = 5Solution
d = {0, 3, 5}
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