(3x^2y+4xy^2+y^3)-(-9x^2y+xy^2+y^3)=0

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Solution for (3x^2y+4xy^2+y^3)-(-9x^2y+xy^2+y^3)=0 equation: 


Simplifying
(3x2y + 4xy2 + y3) + -1(-9x2y + xy2 + y3) = 0

Reorder the terms:
(4xy2 + 3x2y + y3) + -1(-9x2y + xy2 + y3) = 0

Remove parenthesis around (4xy2 + 3x2y + y3)
4xy2 + 3x2y + y3 + -1(-9x2y + xy2 + y3) = 0

Reorder the terms:
4xy2 + 3x2y + y3 + -1(xy2 + -9x2y + y3) = 0
4xy2 + 3x2y + y3 + (xy2 * -1 + -9x2y * -1 + y3 * -1) = 0
4xy2 + 3x2y + y3 + (-1xy2 + 9x2y + -1y3) = 0

Reorder the terms:
4xy2 + -1xy2 + 3x2y + 9x2y + y3 + -1y3 = 0

Combine like terms: 4xy2 + -1xy2 = 3xy2
3xy2 + 3x2y + 9x2y + y3 + -1y3 = 0

Combine like terms: 3x2y + 9x2y = 12x2y
3xy2 + 12x2y + y3 + -1y3 = 0

Combine like terms: y3 + -1y3 = 0
3xy2 + 12x2y + 0 = 0
3xy2 + 12x2y = 0

Solving
3xy2 + 12x2y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(y + 4x) = 0

Ignore the factor 3.

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 '(y + 4x)' equal to zero and attempt to solve:

Simplifying
y + 4x = 0

Reorder the terms:
4x + y = 0

Solving
4x + y = 0

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

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y
Solution
x = {-0.25y}

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