(4c+2d)(7c-5d)=

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Solution for (4c+2d)(7c-5d)= equation: 


Simplifying
(4c + 2d)(7c + -5d) = 0

Multiply (4c + 2d) * (7c + -5d)
(4c * (7c + -5d) + 2d * (7c + -5d)) = 0
((7c * 4c + -5d * 4c) + 2d * (7c + -5d)) = 0

Reorder the terms:
((-20cd + 28c2) + 2d * (7c + -5d)) = 0
((-20cd + 28c2) + 2d * (7c + -5d)) = 0
(-20cd + 28c2 + (7c * 2d + -5d * 2d)) = 0
(-20cd + 28c2 + (14cd + -10d2)) = 0

Reorder the terms:
(-20cd + 14cd + 28c2 + -10d2) = 0

Combine like terms: -20cd + 14cd = -6cd
(-6cd + 28c2 + -10d2) = 0

Solving
-6cd + 28c2 + -10d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3cd + 14c2 + -5d2) = 0

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

Ignore the factor 2.

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 '(2c + d)' equal to zero and attempt to solve:

Simplifying
2c + d = 0

Solving
2c + d = 0

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

Add '-1d' to each side of the equation.
2c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
2c + 0 = 0 + -1d
2c = 0 + -1d
Remove the zero:
2c = -1d

Divide each side by '2'.
c = -0.5d

Simplifying
c = -0.5d
Solution
c = {0.7142857143d, -0.5d}

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