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Simplifying -9d + -24 = -3d(d + 8) + -6d Reorder the terms: -24 + -9d = -3d(d + 8) + -6d Reorder the terms: -24 + -9d = -3d(8 + d) + -6d -24 + -9d = (8 * -3d + d * -3d) + -6d -24 + -9d = (-24d + -3d2) + -6d Reorder the terms: -24 + -9d = -24d + -6d + -3d2 Combine like terms: -24d + -6d = -30d -24 + -9d = -30d + -3d2 Solving -24 + -9d = -30d + -3d2 Solving for variable 'd'. Combine like terms: -9d + 30d = 21d -24 + 21d + 3d2 = -30d + -3d2 + 30d + 3d2 Reorder the terms: -24 + 21d + 3d2 = -30d + 30d + -3d2 + 3d2 Combine like terms: -30d + 30d = 0 -24 + 21d + 3d2 = 0 + -3d2 + 3d2 -24 + 21d + 3d2 = -3d2 + 3d2 Combine like terms: -3d2 + 3d2 = 0 -24 + 21d + 3d2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 7d + d2) = 0 Factor a trinomial. 3((-8 + -1d)(1 + -1d)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -1d)' equal to zero and attempt to solve: Simplifying -8 + -1d = 0 Solving -8 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1d = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1d = 0 + 8 -1d = 0 + 8 Combine like terms: 0 + 8 = 8 -1d = 8 Divide each side by '-1'. d = -8 Simplifying d = -8Subproblem 2
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 = 1Solution
d = {-8, 1}
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