(3SD+4F)(4F+3SD)=

Solution for (3SD+4F)(4F+3SD)= equation:

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) = 0

Subproblem 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-1
Subproblem 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-1
Solution
D = {-1.333333333FS-1, -1.333333333FS-1}