15x^3y+5x^2y^2+10xy^3=0

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Solution for 15x^3y+5x^2y^2+10xy^3=0 equation: 


Simplifying
15x3y + 5x2y2 + 10xy3 = 0

Reorder the terms:
10xy3 + 5x2y2 + 15x3y = 0

Solving
10xy3 + 5x2y2 + 15x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5xy'.
5xy(2y2 + xy + 3x2) = 0

Ignore the factor 5.

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

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
2y2 + xy + 3x2 = 0

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

Solving
xy + 3x2 + 2y2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.3333333333xy + x2 + 0.6666666667y2 = 0

Move the constant term to the right:

Add '-0.6666666667y2' to each side of the equation.
0.3333333333xy + x2 + 0.6666666667y2 + -0.6666666667y2 = 0 + -0.6666666667y2

Combine like terms: 0.6666666667y2 + -0.6666666667y2 = 0.0000000000
0.3333333333xy + x2 + 0.0000000000 = 0 + -0.6666666667y2
0.3333333333xy + x2 = 0 + -0.6666666667y2
Remove the zero:
0.3333333333xy + x2 = -0.6666666667y2

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.
0.3333333333xy + x2 + 0.25y2 = -0.6666666667y2 + 0.25y2

Combine like terms: -0.6666666667y2 + 0.25y2 = -0.4166666667y2
0.3333333333xy + x2 + 0.25y2 = -0.4166666667y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = -0.4166666667y2

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.

The solution to this equation could not be determined.

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