(5c-4d)(8c-3d)=0

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Solution for (5c-4d)(8c-3d)=0 equation: 


Simplifying
(5c + -4d)(8c + -3d) = 0

Multiply (5c + -4d) * (8c + -3d)
(5c * (8c + -3d) + -4d * (8c + -3d)) = 0
((8c * 5c + -3d * 5c) + -4d * (8c + -3d)) = 0

Reorder the terms:
((-15cd + 40c2) + -4d * (8c + -3d)) = 0
((-15cd + 40c2) + -4d * (8c + -3d)) = 0
(-15cd + 40c2 + (8c * -4d + -3d * -4d)) = 0
(-15cd + 40c2 + (-32cd + 12d2)) = 0

Reorder the terms:
(-15cd + -32cd + 40c2 + 12d2) = 0

Combine like terms: -15cd + -32cd = -47cd
(-47cd + 40c2 + 12d2) = 0

Solving
-47cd + 40c2 + 12d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5c + -4d)(8c + -3d) = 0


Subproblem 1
Set the factor '(5c + -4d)' equal to zero and attempt to solve:

Simplifying
5c + -4d = 0

Solving
5c + -4d = 0

Move all terms containing c to the left, all other terms to the right.

Add '4d' to each side of the equation.
5c + -4d + 4d = 0 + 4d

Combine like terms: -4d + 4d = 0
5c + 0 = 0 + 4d
5c = 0 + 4d
Remove the zero:
5c = 4d

Divide each side by '5'.
c = 0.8d

Simplifying
c = 0.8d

Subproblem 2
Set the factor '(8c + -3d)' equal to zero and attempt to solve:

Simplifying
8c + -3d = 0

Solving
8c + -3d = 0

Move all terms containing c to the left, all other terms to the right.

Add '3d' to each side of the equation.
8c + -3d + 3d = 0 + 3d

Combine like terms: -3d + 3d = 0
8c + 0 = 0 + 3d
8c = 0 + 3d
Remove the zero:
8c = 3d

Divide each side by '8'.
c = 0.375d

Simplifying
c = 0.375d
Solution
c = {0.8d, 0.375d}

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