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Simplifying (6x^{4}y^{3}+ 9x^{3}y^{2}) + (3x^{3}y^{3}+ -2x^{3}y^{2}+ -7xy) = 0 Reorder the terms: (9x^{3}y^{2}+ 6x^{4}y^{3}) + (3x^{3}y^{3}+ -2x^{3}y^{2}+ -7xy) = 0 Remove parenthesis around (9x^{3}y^{2}+ 6x^{4}y^{3}) 9x^{3}y^{2}+ 6x^{4}y^{3}+ (3x^{3}y^{3}+ -2x^{3}y^{2}+ -7xy) = 0 Reorder the terms: 9x^{3}y^{2}+ 6x^{4}y^{3}+ (-7xy + -2x^{3}y^{2}+ 3x^{3}y^{3}) = 0 Remove parenthesis around (-7xy + -2x^{3}y^{2}+ 3x^{3}y^{3}) 9x^{3}y^{2}+ 6x^{4}y^{3}+ -7xy + -2x^{3}y^{2}+ 3x^{3}y^{3}= 0 Reorder the terms: -7xy + 9x^{3}y^{2}+ -2x^{3}y^{2}+ 3x^{3}y^{3}+ 6x^{4}y^{3}= 0 Combine like terms: 9x^{3}y^{2}+ -2x^{3}y^{2}= 7x^{3}y^{2}-7xy + 7x^{3}y^{2}+ 3x^{3}y^{3}+ 6x^{4}y^{3}= 0 Solving -7xy + 7x^{3}y^{2}+ 3x^{3}y^{3}+ 6x^{4}y^{3}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'xy'. xy(-7 + 7x^{2}y + 3x^{2}y^{2}+ 6x^{3}y^{2}) = 0## Subproblem 1

Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 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 '(-7 + 7x^{2}y + 3x^{2}y^{2}+ 6x^{3}y^{2})' equal to zero and attempt to solve: Simplifying -7 + 7x^{2}y + 3x^{2}y^{2}+ 6x^{3}y^{2}= 0 Solving -7 + 7x^{2}y + 3x^{2}y^{2}+ 6x^{3}y^{2}= 0 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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