4yx^2+32xy^2-36y^3=0

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Solution for 4yx^2+32xy^2-36y^3=0 equation: 


Simplifying
4yx2 + 32xy2 + -36y3 = 0

Reorder the terms:
32xy2 + 4x2y + -36y3 = 0

Solving
32xy2 + 4x2y + -36y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(8xy + x2 + -9y2) = 0

Factor a trinomial.
4y((x + -1y)(x + 9y)) = 0

Ignore the factor 4.

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 '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

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

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

Simplifying
x = y

Subproblem 3
Set the factor '(x + 9y)' equal to zero and attempt to solve:

Simplifying
x + 9y = 0

Solving
x + 9y = 0

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

Add '-9y' to each side of the equation.
x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
x + 0 = 0 + -9y
x = 0 + -9y
Remove the zero:
x = -9y

Simplifying
x = -9y
Solution
x = {y, -9y}

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