36x^4y+15x^3y^2-9x^2y^3=0

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Solution for 36x^4y+15x^3y^2-9x^2y^3=0 equation: 


Simplifying
36x4y + 15x3y2 + -9x2y3 = 0

Reorder the terms:
-9x2y3 + 15x3y2 + 36x4y = 0

Solving
-9x2y3 + 15x3y2 + 36x4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2y'.
3x2y(-3y2 + 5xy + 12x2) = 0

Factor a trinomial.
3x2y((-3y + -4x)(y + -3x)) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
-3y + -4x = 0

Reorder the terms:
-4x + -3y = 0

Solving
-4x + -3y = 0

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

Add '3y' to each side of the equation.
-4x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
-4x + 0 = 0 + 3y
-4x = 0 + 3y
Remove the zero:
-4x = 3y

Divide each side by '-4'.
x = -0.75y

Simplifying
x = -0.75y

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

Simplifying
y + -3x = 0

Reorder the terms:
-3x + y = 0

Solving
-3x + y = 0

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

Add '-1y' to each side of the equation.
-3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-3x + 0 = 0 + -1y
-3x = 0 + -1y
Remove the zero:
-3x = -1y

Divide each side by '-3'.
x = 0.3333333333y

Simplifying
x = 0.3333333333y
Solution
x = {-0.75y, 0.3333333333y}

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