36x^4y^2+33x^3y^3-45x^2y^4=0

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Solution for 36x^4y^2+33x^3y^3-45x^2y^4=0 equation: 


Simplifying
36x4y2 + 33x3y3 + -45x2y4 = 0

Reorder the terms:
-45x2y4 + 33x3y3 + 36x4y2 = 0

Solving
-45x2y4 + 33x3y3 + 36x4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2y2'.
3x2y2(-15y2 + 11xy + 12x2) = 0

Factor a trinomial.
3x2y2((-5y + -3x)(3y + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2y2' equal to zero and attempt to solve:

Simplifying
x2y2 = 0

Solving
x2y2 = 0

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

Simplifying
x2y2 = 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 '(-5y + -3x)' equal to zero and attempt to solve:

Simplifying
-5y + -3x = 0

Reorder the terms:
-3x + -5y = 0

Solving
-3x + -5y = 0

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

Add '5y' to each side of the equation.
-3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
-3x + 0 = 0 + 5y
-3x = 0 + 5y
Remove the zero:
-3x = 5y

Divide each side by '-3'.
x = -1.666666667y

Simplifying
x = -1.666666667y

Subproblem 3
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
Solution
x = {-1.666666667y, 0.75y}

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