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Simplifying (4d + 3)(7d + -5) = 0 Reorder the terms: (3 + 4d)(7d + -5) = 0 Reorder the terms: (3 + 4d)(-5 + 7d) = 0 Multiply (3 + 4d) * (-5 + 7d) (3(-5 + 7d) + 4d * (-5 + 7d)) = 0 ((-5 * 3 + 7d * 3) + 4d * (-5 + 7d)) = 0 ((-15 + 21d) + 4d * (-5 + 7d)) = 0 (-15 + 21d + (-5 * 4d + 7d * 4d)) = 0 (-15 + 21d + (-20d + 28d2)) = 0 Combine like terms: 21d + -20d = 1d (-15 + 1d + 28d2) = 0 Solving -15 + 1d + 28d2 = 0 Solving for variable 'd'. Factor a trinomial. (-3 + -4d)(5 + -7d) = 0Subproblem 1
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 = -0.75Subproblem 2
Set the factor '(5 + -7d)' equal to zero and attempt to solve: Simplifying 5 + -7d = 0 Solving 5 + -7d = 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 + -7d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7d = 0 + -5 -7d = 0 + -5 Combine like terms: 0 + -5 = -5 -7d = -5 Divide each side by '-7'. d = 0.7142857143 Simplifying d = 0.7142857143Solution
d = {-0.75, 0.7142857143}
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