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Simplifying 2d2 + 3d = 54 Reorder the terms: 3d + 2d2 = 54 Solving 3d + 2d2 = 54 Solving for variable 'd'. Reorder the terms: -54 + 3d + 2d2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 3d + 2d2 = 0 Factor a trinomial. (-6 + -1d)(9 + -2d) = 0Subproblem 1
Set the factor '(-6 + -1d)' equal to zero and attempt to solve: Simplifying -6 + -1d = 0 Solving -6 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1d = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1d = 0 + 6 -1d = 0 + 6 Combine like terms: 0 + 6 = 6 -1d = 6 Divide each side by '-1'. d = -6 Simplifying d = -6Subproblem 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 = {-6, 4.5}
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