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Simplifying (3d + 5)(d + -7) = 0 Reorder the terms: (5 + 3d)(d + -7) = 0 Reorder the terms: (5 + 3d)(-7 + d) = 0 Multiply (5 + 3d) * (-7 + d) (5(-7 + d) + 3d * (-7 + d)) = 0 ((-7 * 5 + d * 5) + 3d * (-7 + d)) = 0 ((-35 + 5d) + 3d * (-7 + d)) = 0 (-35 + 5d + (-7 * 3d + d * 3d)) = 0 (-35 + 5d + (-21d + 3d2)) = 0 Combine like terms: 5d + -21d = -16d (-35 + -16d + 3d2) = 0 Solving -35 + -16d + 3d2 = 0 Solving for variable 'd'. Factor a trinomial. (-5 + -3d)(7 + -1d) = 0Subproblem 1
Set the factor '(-5 + -3d)' equal to zero and attempt to solve: Simplifying -5 + -3d = 0 Solving -5 + -3d = 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 + -3d = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3d = 0 + 5 -3d = 0 + 5 Combine like terms: 0 + 5 = 5 -3d = 5 Divide each side by '-3'. d = -1.666666667 Simplifying d = -1.666666667Subproblem 2
Set the factor '(7 + -1d)' equal to zero and attempt to solve: Simplifying 7 + -1d = 0 Solving 7 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1d = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1d = 0 + -7 -1d = 0 + -7 Combine like terms: 0 + -7 = -7 -1d = -7 Divide each side by '-1'. d = 7 Simplifying d = 7Solution
d = {-1.666666667, 7}
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