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

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


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

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

Reorder the terms:
((-25cd + 35c2) + -2d * (7c + -5d)) = 0
((-25cd + 35c2) + -2d * (7c + -5d)) = 0
(-25cd + 35c2 + (7c * -2d + -5d * -2d)) = 0
(-25cd + 35c2 + (-14cd + 10d2)) = 0

Reorder the terms:
(-25cd + -14cd + 35c2 + 10d2) = 0

Combine like terms: -25cd + -14cd = -39cd
(-39cd + 35c2 + 10d2) = 0

Solving
-39cd + 35c2 + 10d2 = 0

Solving for variable 'c'.

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


Subproblem 1
Set the factor '(7c + -5d)' equal to zero and attempt to solve:

Simplifying
7c + -5d = 0

Solving
7c + -5d = 0

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

Add '5d' to each side of the equation.
7c + -5d + 5d = 0 + 5d

Combine like terms: -5d + 5d = 0
7c + 0 = 0 + 5d
7c = 0 + 5d
Remove the zero:
7c = 5d

Divide each side by '7'.
c = 0.7142857143d

Simplifying
c = 0.7142857143d

Subproblem 2
Set the factor '(5c + -2d)' equal to zero and attempt to solve:

Simplifying
5c + -2d = 0

Solving
5c + -2d = 0

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

Add '2d' to each side of the equation.
5c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
5c + 0 = 0 + 2d
5c = 0 + 2d
Remove the zero:
5c = 2d

Divide each side by '5'.
c = 0.4d

Simplifying
c = 0.4d
Solution
c = {0.7142857143d, 0.4d}

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