10x^2y+7xy^2+y^3=0

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Solution for 10x^2y+7xy^2+y^3=0 equation: 


Simplifying
10x2y + 7xy2 + y3 = 0

Reorder the terms:
7xy2 + 10x2y + y3 = 0

Solving
7xy2 + 10x2y + y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(7xy + 10x2 + y2) = 0

Factor a trinomial.
y((5x + y)(2x + y)) = 0


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

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

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 '(5x + y)' equal to zero and attempt to solve:

Simplifying
5x + y = 0

Solving
5x + y = 0

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

Add '-1y' to each side of the equation.
5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
5x + 0 = 0 + -1y
5x = 0 + -1y
Remove the zero:
5x = -1y

Divide each side by '5'.
x = -0.2y

Simplifying
x = -0.2y

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

Simplifying
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 = {-0.2y, -0.5y}

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