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Simplifying (d + 5)(d + -7) = 0 Reorder the terms: (5 + d)(d + -7) = 0 Reorder the terms: (5 + d)(-7 + d) = 0 Multiply (5 + d) * (-7 + d) (5(-7 + d) + d(-7 + d)) = 0 ((-7 * 5 + d * 5) + d(-7 + d)) = 0 ((-35 + 5d) + d(-7 + d)) = 0 (-35 + 5d + (-7 * d + d * d)) = 0 (-35 + 5d + (-7d + d2)) = 0 Combine like terms: 5d + -7d = -2d (-35 + -2d + d2) = 0 Solving -35 + -2d + d2 = 0 Solving for variable 'd'. Factor a trinomial. (-5 + -1d)(7 + -1d) = 0Subproblem 1
Set the factor '(-5 + -1d)' equal to zero and attempt to solve: Simplifying -5 + -1d = 0 Solving -5 + -1d = 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 + -1d = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1d = 0 + 5 -1d = 0 + 5 Combine like terms: 0 + 5 = 5 -1d = 5 Divide each side by '-1'. d = -5 Simplifying d = -5Subproblem 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 = {-5, 7}
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