10x^3y+25x^2y^2+10xy^3=0

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Solution for 10x^3y+25x^2y^2+10xy^3=0 equation: 


Simplifying
10x3y + 25x2y2 + 10xy3 = 0

Reorder the terms:
10xy3 + 25x2y2 + 10x3y = 0

Solving
10xy3 + 25x2y2 + 10x3y = 0

Solving for variable 'x'.

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

Factor a trinomial.
5xy((2y + x)(y + 2x)) = 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 '(2y + x)' equal to zero and attempt to solve:

Simplifying
2y + x = 0

Reorder the terms:
x + 2y = 0

Solving
x + 2y = 0

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

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y

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

Simplifying
y + 2x = 0

Reorder the terms:
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {-2y, -0.5y}

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