3c^2+9cd-54d^2=0

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Solution for 3c^2+9cd-54d^2=0 equation: 


Simplifying
3c2 + 9cd + -54d2 = 0

Reorder the terms:
9cd + 3c2 + -54d2 = 0

Solving
9cd + 3c2 + -54d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3cd + c2 + -18d2) = 0

Factor a trinomial.
3((c + -3d)(c + 6d)) = 0

Ignore the factor 3.

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

Simplifying
c + -3d = 0

Solving
c + -3d = 0

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

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

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

Simplifying
c = 3d

Subproblem 2
Set the factor '(c + 6d)' equal to zero and attempt to solve:

Simplifying
c + 6d = 0

Solving
c + 6d = 0

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

Add '-6d' to each side of the equation.
c + 6d + -6d = 0 + -6d

Combine like terms: 6d + -6d = 0
c + 0 = 0 + -6d
c = 0 + -6d
Remove the zero:
c = -6d

Simplifying
c = -6d
Solution
c = {3d, -6d}

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