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Simplifying 24d2 + -6d + -30 = 0 Reorder the terms: -30 + -6d + 24d2 = 0 Solving -30 + -6d + 24d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + -1d + 4d2) = 0 Factor a trinomial. 6((-1 + -1d)(5 + -4d)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1d)' equal to zero and attempt to solve: Simplifying -1 + -1d = 0 Solving -1 + -1d = 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 + -1d = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1d = 0 + 1 -1d = 0 + 1 Combine like terms: 0 + 1 = 1 -1d = 1 Divide each side by '-1'. d = -1 Simplifying d = -1Subproblem 2
Set the factor '(5 + -4d)' equal to zero and attempt to solve: Simplifying 5 + -4d = 0 Solving 5 + -4d = 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 + -4d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4d = 0 + -5 -4d = 0 + -5 Combine like terms: 0 + -5 = -5 -4d = -5 Divide each side by '-4'. d = 1.25 Simplifying d = 1.25Solution
d = {-1, 1.25}
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