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Simplifying (6d + 2)(7d + -5) = 0 Reorder the terms: (2 + 6d)(7d + -5) = 0 Reorder the terms: (2 + 6d)(-5 + 7d) = 0 Multiply (2 + 6d) * (-5 + 7d) (2(-5 + 7d) + 6d * (-5 + 7d)) = 0 ((-5 * 2 + 7d * 2) + 6d * (-5 + 7d)) = 0 ((-10 + 14d) + 6d * (-5 + 7d)) = 0 (-10 + 14d + (-5 * 6d + 7d * 6d)) = 0 (-10 + 14d + (-30d + 42d2)) = 0 Combine like terms: 14d + -30d = -16d (-10 + -16d + 42d2) = 0 Solving -10 + -16d + 42d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -8d + 21d2) = 0 Factor a trinomial. 2((-1 + -3d)(5 + -7d)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3d)' equal to zero and attempt to solve: Simplifying -1 + -3d = 0 Solving -1 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3d = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3d = 0 + 1 -3d = 0 + 1 Combine like terms: 0 + 1 = 1 -3d = 1 Divide each side by '-3'. d = -0.3333333333 Simplifying d = -0.3333333333Subproblem 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 = {-0.3333333333, 0.7142857143}
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