6c^4+45c^3d+54c^2d^2=0

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Solution for 6c^4+45c^3d+54c^2d^2=0 equation: 


Simplifying
6c4 + 45c3d + 54c2d2 = 0

Reorder the terms:
54c2d2 + 45c3d + 6c4 = 0

Solving
54c2d2 + 45c3d + 6c4 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3c2'.
3c2(18d2 + 15cd + 2c2) = 0

Factor a trinomial.
3c2((6d + c)(3d + 2c)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve:

Simplifying
c2 = 0

Solving
c2 = 0

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

Simplifying
c2 = 0

Take the square root of each side:
c = {0}

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

Simplifying
6d + c = 0

Reorder the terms:
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

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

Simplifying
3d + 2c = 0

Reorder the terms:
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, -6d, -1.5d}

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