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Simplifying (3d + 5)(2 + -4d) = 0 Reorder the terms: (5 + 3d)(2 + -4d) = 0 Multiply (5 + 3d) * (2 + -4d) (5(2 + -4d) + 3d * (2 + -4d)) = 0 ((2 * 5 + -4d * 5) + 3d * (2 + -4d)) = 0 ((10 + -20d) + 3d * (2 + -4d)) = 0 (10 + -20d + (2 * 3d + -4d * 3d)) = 0 (10 + -20d + (6d + -12d2)) = 0 Combine like terms: -20d + 6d = -14d (10 + -14d + -12d2) = 0 Solving 10 + -14d + -12d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -7d + -6d2) = 0 Factor a trinomial. 2((1 + -2d)(5 + 3d)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2d)' equal to zero and attempt to solve: Simplifying 1 + -2d = 0 Solving 1 + -2d = 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 + -2d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2d = 0 + -1 -2d = 0 + -1 Combine like terms: 0 + -1 = -1 -2d = -1 Divide each side by '-2'. d = 0.5 Simplifying d = 0.5Subproblem 2
Set the factor '(5 + 3d)' equal to zero and attempt to solve: Simplifying 5 + 3d = 0 Solving 5 + 3d = 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 + 3d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3d = 0 + -5 3d = 0 + -5 Combine like terms: 0 + -5 = -5 3d = -5 Divide each side by '3'. d = -1.666666667 Simplifying d = -1.666666667Solution
d = {0.5, -1.666666667}
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