x^3+x^2y+xy^2=0

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


Simplifying
x3 + x2y + xy2 = 0

Reorder the terms:
xy2 + x2y + x3 = 0

Solving
xy2 + x2y + x3 = 0

Solving for variable 'x'.

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


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 '(y2 + xy + x2)' equal to zero and attempt to solve:

Simplifying
y2 + xy + x2 = 0

Reorder the terms:
xy + x2 + y2 = 0

Solving
xy + x2 + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1y2' to each side of the equation.
xy + x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
xy + x2 + 0 = 0 + -1y2
xy + x2 = 0 + -1y2
Remove the zero:
xy + x2 = -1y2

The x term is xy.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
xy + x2 + 0.25y2 = -1y2 + 0.25y2

Combine like terms: -1y2 + 0.25y2 = -0.75y2
xy + x2 + 0.25y2 = -0.75y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = -0.75y2

Can't calculate square root of the right side.

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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