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Simplifying (3d + -12)(10 + -5d) = 0 Reorder the terms: (-12 + 3d)(10 + -5d) = 0 Multiply (-12 + 3d) * (10 + -5d) (-12(10 + -5d) + 3d * (10 + -5d)) = 0 ((10 * -12 + -5d * -12) + 3d * (10 + -5d)) = 0 ((-120 + 60d) + 3d * (10 + -5d)) = 0 (-120 + 60d + (10 * 3d + -5d * 3d)) = 0 (-120 + 60d + (30d + -15d2)) = 0 Combine like terms: 60d + 30d = 90d (-120 + 90d + -15d2) = 0 Solving -120 + 90d + -15d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '15'. 15(-8 + 6d + -1d2) = 0 Factor a trinomial. 15((-4 + d)(2 + -1d)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + d)' equal to zero and attempt to solve: Simplifying -4 + d = 0 Solving -4 + d = 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 + d = 0 + 4 Combine like terms: -4 + 4 = 0 0 + d = 0 + 4 d = 0 + 4 Combine like terms: 0 + 4 = 4 d = 4 Simplifying d = 4Subproblem 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 = 2Solution
d = {4, 2}
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