(3c+d)(7c-6d)=

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Solution for (3c+d)(7c-6d)= equation: 


Simplifying
(3c + d)(7c + -6d) = 0

Multiply (3c + d) * (7c + -6d)
(3c * (7c + -6d) + d(7c + -6d)) = 0
((7c * 3c + -6d * 3c) + d(7c + -6d)) = 0

Reorder the terms:
((-18cd + 21c2) + d(7c + -6d)) = 0
((-18cd + 21c2) + d(7c + -6d)) = 0
(-18cd + 21c2 + (7c * d + -6d * d)) = 0
(-18cd + 21c2 + (7cd + -6d2)) = 0

Reorder the terms:
(-18cd + 7cd + 21c2 + -6d2) = 0

Combine like terms: -18cd + 7cd = -11cd
(-11cd + 21c2 + -6d2) = 0

Solving
-11cd + 21c2 + -6d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(7c + -6d)(3c + d) = 0


Subproblem 1
Set the factor '(7c + -6d)' equal to zero and attempt to solve:

Simplifying
7c + -6d = 0

Solving
7c + -6d = 0

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

Add '6d' to each side of the equation.
7c + -6d + 6d = 0 + 6d

Combine like terms: -6d + 6d = 0
7c + 0 = 0 + 6d
7c = 0 + 6d
Remove the zero:
7c = 6d

Divide each side by '7'.
c = 0.8571428571d

Simplifying
c = 0.8571428571d

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

Simplifying
3c + d = 0

Solving
3c + d = 0

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

Add '-1d' to each side of the equation.
3c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
3c + 0 = 0 + -1d
3c = 0 + -1d
Remove the zero:
3c = -1d

Divide each side by '3'.
c = -0.3333333333d

Simplifying
c = -0.3333333333d
Solution
c = {0.8571428571d, -0.3333333333d}

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