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Simplifying 2d2 + 12d + 13 = -2 + d Reorder the terms: 13 + 12d + 2d2 = -2 + d Solving 13 + 12d + 2d2 = -2 + d Solving for variable 'd'. Reorder the terms: 13 + 2 + 12d + -1d + 2d2 = -2 + d + 2 + -1d Combine like terms: 13 + 2 = 15 15 + 12d + -1d + 2d2 = -2 + d + 2 + -1d Combine like terms: 12d + -1d = 11d 15 + 11d + 2d2 = -2 + d + 2 + -1d Reorder the terms: 15 + 11d + 2d2 = -2 + 2 + d + -1d Combine like terms: -2 + 2 = 0 15 + 11d + 2d2 = 0 + d + -1d 15 + 11d + 2d2 = d + -1d Combine like terms: d + -1d = 0 15 + 11d + 2d2 = 0 Factor a trinomial. (3 + d)(5 + 2d) = 0Subproblem 1
Set the factor '(3 + d)' equal to zero and attempt to solve: Simplifying 3 + d = 0 Solving 3 + d = 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 + d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + d = 0 + -3 d = 0 + -3 Combine like terms: 0 + -3 = -3 d = -3 Simplifying d = -3Subproblem 2
Set the factor '(5 + 2d)' equal to zero and attempt to solve: Simplifying 5 + 2d = 0 Solving 5 + 2d = 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 + 2d = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2d = 0 + -5 2d = 0 + -5 Combine like terms: 0 + -5 = -5 2d = -5 Divide each side by '2'. d = -2.5 Simplifying d = -2.5Solution
d = {-3, -2.5}
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