(5c-3d)(7c-2d)=0

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Solution for (5c-3d)(7c-2d)=0 equation: 


Simplifying
(5c + -3d)(7c + -2d) = 0

Multiply (5c + -3d) * (7c + -2d)
(5c * (7c + -2d) + -3d * (7c + -2d)) = 0
((7c * 5c + -2d * 5c) + -3d * (7c + -2d)) = 0

Reorder the terms:
((-10cd + 35c2) + -3d * (7c + -2d)) = 0
((-10cd + 35c2) + -3d * (7c + -2d)) = 0
(-10cd + 35c2 + (7c * -3d + -2d * -3d)) = 0
(-10cd + 35c2 + (-21cd + 6d2)) = 0

Reorder the terms:
(-10cd + -21cd + 35c2 + 6d2) = 0

Combine like terms: -10cd + -21cd = -31cd
(-31cd + 35c2 + 6d2) = 0

Solving
-31cd + 35c2 + 6d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5c + -3d)(7c + -2d) = 0


Subproblem 1
Set the factor '(5c + -3d)' equal to zero and attempt to solve:

Simplifying
5c + -3d = 0

Solving
5c + -3d = 0

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

Add '3d' to each side of the equation.
5c + -3d + 3d = 0 + 3d

Combine like terms: -3d + 3d = 0
5c + 0 = 0 + 3d
5c = 0 + 3d
Remove the zero:
5c = 3d

Divide each side by '5'.
c = 0.6d

Simplifying
c = 0.6d

Subproblem 2
Set the factor '(7c + -2d)' equal to zero and attempt to solve:

Simplifying
7c + -2d = 0

Solving
7c + -2d = 0

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

Add '2d' to each side of the equation.
7c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
7c + 0 = 0 + 2d
7c = 0 + 2d
Remove the zero:
7c = 2d

Divide each side by '7'.
c = 0.2857142857d

Simplifying
c = 0.2857142857d
Solution
c = {0.6d, 0.2857142857d}

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