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Simplifying (8d + -5)(2d + 3) = 0 Reorder the terms: (-5 + 8d)(2d + 3) = 0 Reorder the terms: (-5 + 8d)(3 + 2d) = 0 Multiply (-5 + 8d) * (3 + 2d) (-5(3 + 2d) + 8d * (3 + 2d)) = 0 ((3 * -5 + 2d * -5) + 8d * (3 + 2d)) = 0 ((-15 + -10d) + 8d * (3 + 2d)) = 0 (-15 + -10d + (3 * 8d + 2d * 8d)) = 0 (-15 + -10d + (24d + 16d2)) = 0 Combine like terms: -10d + 24d = 14d (-15 + 14d + 16d2) = 0 Solving -15 + 14d + 16d2 = 0 Solving for variable 'd'. Factor a trinomial. (-3 + -2d)(5 + -8d) = 0Subproblem 1
Set the factor '(-3 + -2d)' equal to zero and attempt to solve: Simplifying -3 + -2d = 0 Solving -3 + -2d = 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 + -2d = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2d = 0 + 3 -2d = 0 + 3 Combine like terms: 0 + 3 = 3 -2d = 3 Divide each side by '-2'. d = -1.5 Simplifying d = -1.5Subproblem 2
Set the factor '(5 + -8d)' equal to zero and attempt to solve: Simplifying 5 + -8d = 0 Solving 5 + -8d = 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 + -8d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8d = 0 + -5 -8d = 0 + -5 Combine like terms: 0 + -5 = -5 -8d = -5 Divide each side by '-8'. d = 0.625 Simplifying d = 0.625Solution
d = {-1.5, 0.625}
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