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

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


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

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

Reorder the terms:
((cd + 5c2) + 7d * (5c + d)) = 0
((cd + 5c2) + 7d * (5c + d)) = 0
(cd + 5c2 + (5c * 7d + d * 7d)) = 0
(cd + 5c2 + (35cd + 7d2)) = 0

Reorder the terms:
(cd + 35cd + 5c2 + 7d2) = 0

Combine like terms: cd + 35cd = 36cd
(36cd + 5c2 + 7d2) = 0

Solving
36cd + 5c2 + 7d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(5c + d)(c + 7d) = 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 '(c + 7d)' equal to zero and attempt to solve:

Simplifying
c + 7d = 0

Solving
c + 7d = 0

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

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

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

Simplifying
c = -7d
Solution
c = {-0.2d, -7d}

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