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Simplifying 3(d + -3) + 2d(d + -3) = 18 Reorder the terms: 3(-3 + d) + 2d(d + -3) = 18 (-3 * 3 + d * 3) + 2d(d + -3) = 18 (-9 + 3d) + 2d(d + -3) = 18 Reorder the terms: -9 + 3d + 2d(-3 + d) = 18 -9 + 3d + (-3 * 2d + d * 2d) = 18 -9 + 3d + (-6d + 2d2) = 18 Combine like terms: 3d + -6d = -3d -9 + -3d + 2d2 = 18 Solving -9 + -3d + 2d2 = 18 Solving for variable 'd'. Reorder the terms: -9 + -18 + -3d + 2d2 = 18 + -18 Combine like terms: -9 + -18 = -27 -27 + -3d + 2d2 = 18 + -18 Combine like terms: 18 + -18 = 0 -27 + -3d + 2d2 = 0 Factor a trinomial. (-3 + -1d)(9 + -2d) = 0Subproblem 1
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 = -3Subproblem 2
Set the factor '(9 + -2d)' equal to zero and attempt to solve: Simplifying 9 + -2d = 0 Solving 9 + -2d = 0 Move all terms containing d to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2d = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2d = 0 + -9 -2d = 0 + -9 Combine like terms: 0 + -9 = -9 -2d = -9 Divide each side by '-2'. d = 4.5 Simplifying d = 4.5Solution
d = {-3, 4.5}
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