30x^4y+39x^3y^2-9x^2y^3=0

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Solution for 30x^4y+39x^3y^2-9x^2y^3=0 equation: 


Simplifying
30x4y + 39x3y2 + -9x2y3 = 0

Reorder the terms:
-9x2y3 + 39x3y2 + 30x4y = 0

Solving
-9x2y3 + 39x3y2 + 30x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2y'.
3x2y(-3y2 + 13xy + 10x2) = 0

Factor a trinomial.
3x2y((-3y + -2x)(y + -5x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2y' equal to zero and attempt to solve:

Simplifying
x2y = 0

Solving
x2y = 0

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

Simplifying
x2y = 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 '(-3y + -2x)' equal to zero and attempt to solve:

Simplifying
-3y + -2x = 0

Reorder the terms:
-2x + -3y = 0

Solving
-2x + -3y = 0

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

Add '3y' to each side of the equation.
-2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
-2x + 0 = 0 + 3y
-2x = 0 + 3y
Remove the zero:
-2x = 3y

Divide each side by '-2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 3
Set the factor '(y + -5x)' equal to zero and attempt to solve:

Simplifying
y + -5x = 0

Reorder the terms:
-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
Solution
x = {-1.5y, 0.2y}

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