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Simplifying (3d + -5)(d + 2) = 0 Reorder the terms: (-5 + 3d)(d + 2) = 0 Reorder the terms: (-5 + 3d)(2 + d) = 0 Multiply (-5 + 3d) * (2 + d) (-5(2 + d) + 3d * (2 + d)) = 0 ((2 * -5 + d * -5) + 3d * (2 + d)) = 0 ((-10 + -5d) + 3d * (2 + d)) = 0 (-10 + -5d + (2 * 3d + d * 3d)) = 0 (-10 + -5d + (6d + 3d2)) = 0 Combine like terms: -5d + 6d = 1d (-10 + 1d + 3d2) = 0 Solving -10 + 1d + 3d2 = 0 Solving for variable 'd'. Factor a trinomial. (-2 + -1d)(5 + -3d) = 0Subproblem 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 '(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 = {-2, 1.666666667}
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