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Simplifying 12d2 + 8d + -32 = 0 Reorder the terms: -32 + 8d + 12d2 = 0 Solving -32 + 8d + 12d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 2d + 3d2) = 0 Factor a trinomial. 4((-2 + -1d)(4 + -3d)) = 0 Ignore the factor 4.Subproblem 1
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 2
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 = {-2, 1.333333333}
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