-3x^3y+12x^2y^2+63xy^3=0

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Solution for -3x^3y+12x^2y^2+63xy^3=0 equation: 


Simplifying
-3x3y + 12x2y2 + 63xy3 = 0

Reorder the terms:
63xy3 + 12x2y2 + -3x3y = 0

Solving
63xy3 + 12x2y2 + -3x3y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy'.
3xy(21y2 + 4xy + -1x2) = 0

Factor a trinomial.
3xy((7y + -1x)(3y + x)) = 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 '(7y + -1x)' equal to zero and attempt to solve:

Simplifying
7y + -1x = 0

Reorder the terms:
-1x + 7y = 0

Solving
-1x + 7y = 0

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

Add '-7y' to each side of the equation.
-1x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
-1x + 0 = 0 + -7y
-1x = 0 + -7y
Remove the zero:
-1x = -7y

Divide each side by '-1'.
x = 7y

Simplifying
x = 7y

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

Simplifying
3y + x = 0

Reorder the terms:
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 = {7y, -3y}

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