20x^2y^2-60xy^3+45y^4=0

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Solution for 20x^2y^2-60xy^3+45y^4=0 equation:


Simplifying
20x2y2 + -60xy3 + 45y4 = 0

Reorder the terms:
-60xy3 + 20x2y2 + 45y4 = 0

Solving
-60xy3 + 20x2y2 + 45y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(-12xy + 4x2 + 9y2) = 0

Factor a trinomial.
5y2((2x + -3y)(2x + -3y)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. y2 + -1y2 = 0 + -1y2 Remove the zero: 0 = -1y2 Simplifying 0 = -1y2 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 '(2x + -3y)' equal to zero and attempt to solve: Simplifying 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 '(2x + -3y)' equal to zero and attempt to solve: Simplifying 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

Solution

x = {1.5y, 1.5y}

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