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Simplifying (3 + -4d)(2d + -5) = 0 Reorder the terms: (3 + -4d)(-5 + 2d) = 0 Multiply (3 + -4d) * (-5 + 2d) (3(-5 + 2d) + -4d * (-5 + 2d)) = 0 ((-5 * 3 + 2d * 3) + -4d * (-5 + 2d)) = 0 ((-15 + 6d) + -4d * (-5 + 2d)) = 0 (-15 + 6d + (-5 * -4d + 2d * -4d)) = 0 (-15 + 6d + (20d + -8d2)) = 0 Combine like terms: 6d + 20d = 26d (-15 + 26d + -8d2) = 0 Solving -15 + 26d + -8d2 = 0 Solving for variable 'd'. Factor a trinomial. (-5 + 2d)(3 + -4d) = 0Subproblem 1
Set the factor '(-5 + 2d)' equal to zero and attempt to solve: Simplifying -5 + 2d = 0 Solving -5 + 2d = 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 + 2d = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2d = 0 + 5 2d = 0 + 5 Combine like terms: 0 + 5 = 5 2d = 5 Divide each side by '2'. d = 2.5 Simplifying d = 2.5Subproblem 2
Set the factor '(3 + -4d)' equal to zero and attempt to solve: Simplifying 3 + -4d = 0 Solving 3 + -4d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4d = 0 + -3 -4d = 0 + -3 Combine like terms: 0 + -3 = -3 -4d = -3 Divide each side by '-4'. d = 0.75 Simplifying d = 0.75Solution
d = {2.5, 0.75}
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