(2c+3d)(7c-6d)=0

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Solution for (2c+3d)(7c-6d)=0 equation: 


Simplifying
(2c + 3d)(7c + -6d) = 0

Multiply (2c + 3d) * (7c + -6d)
(2c * (7c + -6d) + 3d * (7c + -6d)) = 0
((7c * 2c + -6d * 2c) + 3d * (7c + -6d)) = 0

Reorder the terms:
((-12cd + 14c2) + 3d * (7c + -6d)) = 0
((-12cd + 14c2) + 3d * (7c + -6d)) = 0
(-12cd + 14c2 + (7c * 3d + -6d * 3d)) = 0
(-12cd + 14c2 + (21cd + -18d2)) = 0

Reorder the terms:
(-12cd + 21cd + 14c2 + -18d2) = 0

Combine like terms: -12cd + 21cd = 9cd
(9cd + 14c2 + -18d2) = 0

Solving
9cd + 14c2 + -18d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(7c + -6d)(2c + 3d) = 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 '(2c + 3d)' equal to zero and attempt to solve:

Simplifying
2c + 3d = 0

Solving
2c + 3d = 0

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

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

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

Divide each side by '2'.
c = -1.5d

Simplifying
c = -1.5d
Solution
c = {0.8571428571d, -1.5d}

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