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Simplifying (4d + -9)(2d + -3) = 0 Reorder the terms: (-9 + 4d)(2d + -3) = 0 Reorder the terms: (-9 + 4d)(-3 + 2d) = 0 Multiply (-9 + 4d) * (-3 + 2d) (-9(-3 + 2d) + 4d * (-3 + 2d)) = 0 ((-3 * -9 + 2d * -9) + 4d * (-3 + 2d)) = 0 ((27 + -18d) + 4d * (-3 + 2d)) = 0 (27 + -18d + (-3 * 4d + 2d * 4d)) = 0 (27 + -18d + (-12d + 8d2)) = 0 Combine like terms: -18d + -12d = -30d (27 + -30d + 8d2) = 0 Solving 27 + -30d + 8d2 = 0 Solving for variable 'd'. Factor a trinomial. (3 + -2d)(9 + -4d) = 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 '(9 + -4d)' equal to zero and attempt to solve: Simplifying 9 + -4d = 0 Solving 9 + -4d = 0 Move all terms containing d to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4d = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4d = 0 + -9 -4d = 0 + -9 Combine like terms: 0 + -9 = -9 -4d = -9 Divide each side by '-4'. d = 2.25 Simplifying d = 2.25Solution
d = {1.5, 2.25}
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