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Simplifying 20x^{4}y^{3}+ -45x^{2}y^{3}+ -5x^{2}y^{2}= 0 Reorder the terms: -5x^{2}y^{2}+ -45x^{2}y^{3}+ 20x^{4}y^{3}= 0 Solving -5x^{2}y^{2}+ -45x^{2}y^{3}+ 20x^{4}y^{3}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x^{2}y^{2}'. 5x^{2}y^{2}(-1 + -9y + 4x^{2}y) = 0 Ignore the factor 5.## Subproblem 1

Set the factor 'x^{2}y^{2}' equal to zero and attempt to solve: Simplifying x^{2}y^{2}= 0 Solving x^{2}y^{2}= 0 Move all terms containing x to the left, all other terms to the right. Simplifying x^{2}y^{2}= 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 '(-1 + -9y + 4x^{2}y)' equal to zero and attempt to solve: Simplifying -1 + -9y + 4x^{2}y = 0 Reorder the terms: -1 + 4x^{2}y + -9y = 0 Solving -1 + 4x^{2}y + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 4x^{2}y + 1 + -9y = 0 + 1 Reorder the terms: -1 + 1 + 4x^{2}y + -9y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x^{2}y + -9y = 0 + 1 4x^{2}y + -9y = 0 + 1 Combine like terms: 0 + 1 = 1 4x^{2}y + -9y = 1 Add '9y' to each side of the equation. 4x^{2}y + -9y + 9y = 1 + 9y Combine like terms: -9y + 9y = 0 4x^{2}y + 0 = 1 + 9y 4x^{2}y = 1 + 9y Divide each side by '4y'. x^{2}= 0.25y^{-1}+ 2.25 Simplifying x^{2}= 0.25y^{-1}+ 2.25 Reorder the terms: x^{2}= 2.25 + 0.25y^{-1}The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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