(9c-2d)(3c-7d)=0

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Solution for (9c-2d)(3c-7d)=0 equation: 


Simplifying
(9c + -2d)(3c + -7d) = 0

Multiply (9c + -2d) * (3c + -7d)
(9c * (3c + -7d) + -2d * (3c + -7d)) = 0
((3c * 9c + -7d * 9c) + -2d * (3c + -7d)) = 0

Reorder the terms:
((-63cd + 27c2) + -2d * (3c + -7d)) = 0
((-63cd + 27c2) + -2d * (3c + -7d)) = 0
(-63cd + 27c2 + (3c * -2d + -7d * -2d)) = 0
(-63cd + 27c2 + (-6cd + 14d2)) = 0

Reorder the terms:
(-63cd + -6cd + 27c2 + 14d2) = 0

Combine like terms: -63cd + -6cd = -69cd
(-69cd + 27c2 + 14d2) = 0

Solving
-69cd + 27c2 + 14d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(3c + -7d)(9c + -2d) = 0


Subproblem 1
Set the factor '(3c + -7d)' equal to zero and attempt to solve:

Simplifying
3c + -7d = 0

Solving
3c + -7d = 0

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

Add '7d' to each side of the equation.
3c + -7d + 7d = 0 + 7d

Combine like terms: -7d + 7d = 0
3c + 0 = 0 + 7d
3c = 0 + 7d
Remove the zero:
3c = 7d

Divide each side by '3'.
c = 2.333333333d

Simplifying
c = 2.333333333d

Subproblem 2
Set the factor '(9c + -2d)' equal to zero and attempt to solve:

Simplifying
9c + -2d = 0

Solving
9c + -2d = 0

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

Add '2d' to each side of the equation.
9c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
9c + 0 = 0 + 2d
9c = 0 + 2d
Remove the zero:
9c = 2d

Divide each side by '9'.
c = 0.2222222222d

Simplifying
c = 0.2222222222d
Solution
c = {2.333333333d, 0.2222222222d}

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