4x^3+4xy^2+6xy=0

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Solution for 4x^3+4xy^2+6xy=0 equation: 


Simplifying
4x3 + 4xy2 + 6xy = 0

Reorder the terms:
6xy + 4xy2 + 4x3 = 0

Solving
6xy + 4xy2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3y + 2y2 + 2x2) = 0

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(3y + 2y2 + 2x2)' equal to zero and attempt to solve:

Simplifying
3y + 2y2 + 2x2 = 0

Reorder the terms:
2x2 + 3y + 2y2 = 0

Solving
2x2 + 3y + 2y2 = 0

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

Add '-3y' to each side of the equation.
2x2 + 3y + -3y + 2y2 = 0 + -3y

Combine like terms: 3y + -3y = 0
2x2 + 0 + 2y2 = 0 + -3y
2x2 + 2y2 = 0 + -3y
Remove the zero:
2x2 + 2y2 = -3y

Add '-2y2' to each side of the equation.
2x2 + 2y2 + -2y2 = -3y + -2y2

Combine like terms: 2y2 + -2y2 = 0
2x2 + 0 = -3y + -2y2
2x2 = -3y + -2y2

Divide each side by '2'.
x2 = -1.5y + -1y2

Simplifying
x2 = -1.5y + -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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