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Simplifying (3d + -1)(d + 9) = 0 Reorder the terms: (-1 + 3d)(d + 9) = 0 Reorder the terms: (-1 + 3d)(9 + d) = 0 Multiply (-1 + 3d) * (9 + d) (-1(9 + d) + 3d * (9 + d)) = 0 ((9 * -1 + d * -1) + 3d * (9 + d)) = 0 ((-9 + -1d) + 3d * (9 + d)) = 0 (-9 + -1d + (9 * 3d + d * 3d)) = 0 (-9 + -1d + (27d + 3d2)) = 0 Combine like terms: -1d + 27d = 26d (-9 + 26d + 3d2) = 0 Solving -9 + 26d + 3d2 = 0 Solving for variable 'd'. Factor a trinomial. (-9 + -1d)(1 + -3d) = 0Subproblem 1
Set the factor '(-9 + -1d)' equal to zero and attempt to solve: Simplifying -9 + -1d = 0 Solving -9 + -1d = 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 + -1d = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1d = 0 + 9 -1d = 0 + 9 Combine like terms: 0 + 9 = 9 -1d = 9 Divide each side by '-1'. d = -9 Simplifying d = -9Subproblem 2
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 = 0.3333333333Solution
d = {-9, 0.3333333333}
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