20x^4y^2+18x^3y^3-18x^2y^4=0

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Solution for 20x^4y^2+18x^3y^3-18x^2y^4=0 equation: 


Simplifying
20x4y2 + 18x3y3 + -18x2y4 = 0

Reorder the terms:
-18x2y4 + 18x3y3 + 20x4y2 = 0

Solving
-18x2y4 + 18x3y3 + 20x4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2y2'.
2x2y2(-9y2 + 9xy + 10x2) = 0

Factor a trinomial.
2x2y2((-3y + -2x)(3y + -5x)) = 0

Ignore the factor 2.

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

Simplifying
3y + -5x = 0

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

Solving
-5x + 3y = 0

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

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

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

Divide each side by '-5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {-1.5y, 0.6y}

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