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

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


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

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

Reorder the terms:
((20cd + 35c2) + d(7c + 4d)) = 0
((20cd + 35c2) + d(7c + 4d)) = 0
(20cd + 35c2 + (7c * d + 4d * d)) = 0
(20cd + 35c2 + (7cd + 4d2)) = 0

Reorder the terms:
(20cd + 7cd + 35c2 + 4d2) = 0

Combine like terms: 20cd + 7cd = 27cd
(27cd + 35c2 + 4d2) = 0

Solving
27cd + 35c2 + 4d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5c + d)(7c + 4d) = 0


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

Simplifying
5c + d = 0

Solving
5c + d = 0

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

Add '-1d' to each side of the equation.
5c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
5c + 0 = 0 + -1d
5c = 0 + -1d
Remove the zero:
5c = -1d

Divide each side by '5'.
c = -0.2d

Simplifying
c = -0.2d

Subproblem 2
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
Solution
c = {-0.2d, -0.5714285714d}

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