6x^2y-63xy^2+135y^3=0

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Solution for 6x^2y-63xy^2+135y^3=0 equation: 


Simplifying
6x2y + -63xy2 + 135y3 = 0

Reorder the terms:
-63xy2 + 6x2y + 135y3 = 0

Solving
-63xy2 + 6x2y + 135y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-21xy + 2x2 + 45y2) = 0

Factor a trinomial.
3y((2x + -15y)(x + -3y)) = 0

Ignore the factor 3.

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 '(2x + -15y)' equal to zero and attempt to solve:

Simplifying
2x + -15y = 0

Solving
2x + -15y = 0

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

Add '15y' to each side of the equation.
2x + -15y + 15y = 0 + 15y

Combine like terms: -15y + 15y = 0
2x + 0 = 0 + 15y
2x = 0 + 15y
Remove the zero:
2x = 15y

Divide each side by '2'.
x = 7.5y

Simplifying
x = 7.5y

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '3y' to each side of the equation.
x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y
Solution
x = {7.5y, 3y}

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