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

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


Simplifying
7d(2d + c) + 3c(4d + -1c) = 0

Reorder the terms:
7d(c + 2d) + 3c(4d + -1c) = 0
(c * 7d + 2d * 7d) + 3c(4d + -1c) = 0
(7cd + 14d2) + 3c(4d + -1c) = 0

Reorder the terms:
7cd + 14d2 + 3c(-1c + 4d) = 0
7cd + 14d2 + (-1c * 3c + 4d * 3c) = 0

Reorder the terms:
7cd + 14d2 + (12cd + -3c2) = 0
7cd + 14d2 + (12cd + -3c2) = 0

Reorder the terms:
7cd + 12cd + -3c2 + 14d2 = 0

Combine like terms: 7cd + 12cd = 19cd
19cd + -3c2 + 14d2 = 0

Solving
19cd + -3c2 + 14d2 = 0

Solving for variable 'c'.

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


Subproblem 1
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

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 = {-0.6666666667d, 7d}

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