9c^4d-21c^3d^2+6c^2d^3=0

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Solution for 9c^4d-21c^3d^2+6c^2d^3=0 equation: 


Simplifying
9c4d + -21c3d2 + 6c2d3 = 0

Reorder the terms:
6c2d3 + -21c3d2 + 9c4d = 0

Solving
6c2d3 + -21c3d2 + 9c4d = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3c2d'.
3c2d(2d2 + -7cd + 3c2) = 0

Factor a trinomial.
3c2d((d + -3c)(2d + -1c)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'c2d' equal to zero and attempt to solve:

Simplifying
c2d = 0

Solving
c2d = 0

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

Simplifying
c2d = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(d + -3c)' equal to zero and attempt to solve:

Simplifying
d + -3c = 0

Reorder the terms:
-3c + d = 0

Solving
-3c + d = 0

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

Add '-1d' to each side of the equation.
-3c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
-3c + 0 = 0 + -1d
-3c = 0 + -1d
Remove the zero:
-3c = -1d

Divide each side by '-3'.
c = 0.3333333333d

Simplifying
c = 0.3333333333d

Subproblem 3
Set the factor '(2d + -1c)' equal to zero and attempt to solve:

Simplifying
2d + -1c = 0

Reorder the terms:
-1c + 2d = 0

Solving
-1c + 2d = 0

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

Add '-2d' to each side of the equation.
-1c + 2d + -2d = 0 + -2d

Combine like terms: 2d + -2d = 0
-1c + 0 = 0 + -2d
-1c = 0 + -2d
Remove the zero:
-1c = -2d

Divide each side by '-1'.
c = 2d

Simplifying
c = 2d
Solution
c = {0.3333333333d, 2d}

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