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Simplifying -2d2 + 17d + -28 = 3d2 + -13d + 17 Reorder the terms: -28 + 17d + -2d2 = 3d2 + -13d + 17 Reorder the terms: -28 + 17d + -2d2 = 17 + -13d + 3d2 Solving -28 + 17d + -2d2 = 17 + -13d + 3d2 Solving for variable 'd'. Reorder the terms: -28 + -17 + 17d + 13d + -2d2 + -3d2 = 17 + -13d + 3d2 + -17 + 13d + -3d2 Combine like terms: -28 + -17 = -45 -45 + 17d + 13d + -2d2 + -3d2 = 17 + -13d + 3d2 + -17 + 13d + -3d2 Combine like terms: 17d + 13d = 30d -45 + 30d + -2d2 + -3d2 = 17 + -13d + 3d2 + -17 + 13d + -3d2 Combine like terms: -2d2 + -3d2 = -5d2 -45 + 30d + -5d2 = 17 + -13d + 3d2 + -17 + 13d + -3d2 Reorder the terms: -45 + 30d + -5d2 = 17 + -17 + -13d + 13d + 3d2 + -3d2 Combine like terms: 17 + -17 = 0 -45 + 30d + -5d2 = 0 + -13d + 13d + 3d2 + -3d2 -45 + 30d + -5d2 = -13d + 13d + 3d2 + -3d2 Combine like terms: -13d + 13d = 0 -45 + 30d + -5d2 = 0 + 3d2 + -3d2 -45 + 30d + -5d2 = 3d2 + -3d2 Combine like terms: 3d2 + -3d2 = 0 -45 + 30d + -5d2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 6d + -1d2) = 0 Factor a trinomial. 5((-3 + d)(3 + -1d)) = 0 Ignore the factor 5.Subproblem 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 '(3 + -1d)' equal to zero and attempt to solve: Simplifying 3 + -1d = 0 Solving 3 + -1d = 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 + -1d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d = 0 + -3 -1d = 0 + -3 Combine like terms: 0 + -3 = -3 -1d = -3 Divide each side by '-1'. d = 3 Simplifying d = 3Solution
d = {3, 3}
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