3c^4-12c^3d-36c^2d^2=0

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Solution for 3c^4-12c^3d-36c^2d^2=0 equation: 


Simplifying
3c4 + -12c3d + -36c2d2 = 0

Reorder the terms:
-36c2d2 + -12c3d + 3c4 = 0

Solving
-36c2d2 + -12c3d + 3c4 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3c2'.
3c2(-12d2 + -4cd + c2) = 0

Factor a trinomial.
3c2((-2d + -1c)(6d + -1c)) = 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 '(-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

Subproblem 3
Set the factor '(6d + -1c)' equal to zero and attempt to solve:

Simplifying
6d + -1c = 0

Reorder the terms:
-1c + 6d = 0

Solving
-1c + 6d = 0

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

Add '-6d' to each side of the equation.
-1c + 6d + -6d = 0 + -6d

Combine like terms: 6d + -6d = 0
-1c + 0 = 0 + -6d
-1c = 0 + -6d
Remove the zero:
-1c = -6d

Divide each side by '-1'.
c = 6d

Simplifying
c = 6d
Solution
c = {0, -2d, 6d}

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