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Simplifying (3d + -4)(5d + -6) = 0 Reorder the terms: (-4 + 3d)(5d + -6) = 0 Reorder the terms: (-4 + 3d)(-6 + 5d) = 0 Multiply (-4 + 3d) * (-6 + 5d) (-4(-6 + 5d) + 3d * (-6 + 5d)) = 0 ((-6 * -4 + 5d * -4) + 3d * (-6 + 5d)) = 0 ((24 + -20d) + 3d * (-6 + 5d)) = 0 (24 + -20d + (-6 * 3d + 5d * 3d)) = 0 (24 + -20d + (-18d + 15d2)) = 0 Combine like terms: -20d + -18d = -38d (24 + -38d + 15d2) = 0 Solving 24 + -38d + 15d2 = 0 Solving for variable 'd'. Factor a trinomial. (6 + -5d)(4 + -3d) = 0Subproblem 1
Set the factor '(6 + -5d)' equal to zero and attempt to solve: Simplifying 6 + -5d = 0 Solving 6 + -5d = 0 Move all terms containing d to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5d = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5d = 0 + -6 -5d = 0 + -6 Combine like terms: 0 + -6 = -6 -5d = -6 Divide each side by '-5'. d = 1.2 Simplifying d = 1.2Subproblem 2
Set the factor '(4 + -3d)' equal to zero and attempt to solve: Simplifying 4 + -3d = 0 Solving 4 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3d = 0 + -4 -3d = 0 + -4 Combine like terms: 0 + -4 = -4 -3d = -4 Divide each side by '-3'. d = 1.333333333 Simplifying d = 1.333333333Solution
d = {1.2, 1.333333333}
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