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Simplifying (3SD + 4F)(4F + 3SD) = 0 Reorder the terms: (3DS + 4F)(3DS + 4F) = 0 Multiply (3DS + 4F) * (3DS + 4F) (3DS * (3DS + 4F) + 4F * (3DS + 4F)) = 0 ((3DS * 3DS + 4F * 3DS) + 4F * (3DS + 4F)) = 0 Reorder the terms: ((12DFS + 9D2S2) + 4F * (3DS + 4F)) = 0 ((12DFS + 9D2S2) + 4F * (3DS + 4F)) = 0 (12DFS + 9D2S2 + (3DS * 4F + 4F * 4F)) = 0 (12DFS + 9D2S2 + (12DFS + 16F2)) = 0 Reorder the terms: (12DFS + 12DFS + 9D2S2 + 16F2) = 0 Combine like terms: 12DFS + 12DFS = 24DFS (24DFS + 9D2S2 + 16F2) = 0 Solving 24DFS + 9D2S2 + 16F2 = 0 Solving for variable 'D'. Factor a trinomial. (3DS + 4F)(3DS + 4F) = 0Subproblem 1
Set the factor '(3DS + 4F)' equal to zero and attempt to solve: Simplifying 3DS + 4F = 0 Solving 3DS + 4F = 0 Move all terms containing D to the left, all other terms to the right. Add '-4F' to each side of the equation. 3DS + 4F + -4F = 0 + -4F Combine like terms: 4F + -4F = 0 3DS + 0 = 0 + -4F 3DS = 0 + -4F Remove the zero: 3DS = -4F Divide each side by '3S'. D = -1.333333333FS-1 Simplifying D = -1.333333333FS-1Subproblem 2
Set the factor '(3DS + 4F)' equal to zero and attempt to solve: Simplifying 3DS + 4F = 0 Solving 3DS + 4F = 0 Move all terms containing D to the left, all other terms to the right. Add '-4F' to each side of the equation. 3DS + 4F + -4F = 0 + -4F Combine like terms: 4F + -4F = 0 3DS + 0 = 0 + -4F 3DS = 0 + -4F Remove the zero: 3DS = -4F Divide each side by '3S'. D = -1.333333333FS-1 Simplifying D = -1.333333333FS-1Solution
D = {-1.333333333FS-1, -1.333333333FS-1}
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