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Simplifying 18x3y + -51x2y2 + -42xy3 = 0 Reorder the terms: -42xy3 + -51x2y2 + 18x3y = 0 Solving -42xy3 + -51x2y2 + 18x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3xy'. 3xy(-14y2 + -17xy + 6x2) = 0 Factor a trinomial. 3xy((-2y + -3x)(7y + -2x)) = 0 Ignore the factor 3.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 '(-2y + -3x)' equal to zero and attempt to solve: Simplifying -2y + -3x = 0 Reorder the terms: -3x + -2y = 0 Solving -3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -3x + 0 = 0 + 2y -3x = 0 + 2y Remove the zero: -3x = 2y Divide each side by '-3'. x = -0.6666666667y Simplifying x = -0.6666666667ySubproblem 3
Set the factor '(7y + -2x)' equal to zero and attempt to solve: Simplifying 7y + -2x = 0 Reorder the terms: -2x + 7y = 0 Solving -2x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. -2x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 -2x + 0 = 0 + -7y -2x = 0 + -7y Remove the zero: -2x = -7y Divide each side by '-2'. x = 3.5y Simplifying x = 3.5ySolution
x = {-0.6666666667y, 3.5y}
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