(3c+2d)(7c-4d)=

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Solution for (3c+2d)(7c-4d)= equation: 


Simplifying
(3c + 2d)(7c + -4d) = 0

Multiply (3c + 2d) * (7c + -4d)
(3c * (7c + -4d) + 2d * (7c + -4d)) = 0
((7c * 3c + -4d * 3c) + 2d * (7c + -4d)) = 0

Reorder the terms:
((-12cd + 21c2) + 2d * (7c + -4d)) = 0
((-12cd + 21c2) + 2d * (7c + -4d)) = 0
(-12cd + 21c2 + (7c * 2d + -4d * 2d)) = 0
(-12cd + 21c2 + (14cd + -8d2)) = 0

Reorder the terms:
(-12cd + 14cd + 21c2 + -8d2) = 0

Combine like terms: -12cd + 14cd = 2cd
(2cd + 21c2 + -8d2) = 0

Solving
2cd + 21c2 + -8d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(7c + -4d)(3c + 2d) = 0


Subproblem 1
Set the factor '(7c + -4d)' equal to zero and attempt to solve:

Simplifying
7c + -4d = 0

Solving
7c + -4d = 0

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

Add '4d' to each side of the equation.
7c + -4d + 4d = 0 + 4d

Combine like terms: -4d + 4d = 0
7c + 0 = 0 + 4d
7c = 0 + 4d
Remove the zero:
7c = 4d

Divide each side by '7'.
c = 0.5714285714d

Simplifying
c = 0.5714285714d

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

Simplifying
3c + 2d = 0

Solving
3c + 2d = 0

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

Add '-2d' to each side of the equation.
3c + 2d + -2d = 0 + -2d

Combine like terms: 2d + -2d = 0
3c + 0 = 0 + -2d
3c = 0 + -2d
Remove the zero:
3c = -2d

Divide each side by '3'.
c = -0.6666666667d

Simplifying
c = -0.6666666667d
Solution
c = {0.5714285714d, -0.6666666667d}

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