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Simplifying 3x2 + -27xy + 54y2 = 0 Reorder the terms: -27xy + 3x2 + 54y2 = 0 Solving -27xy + 3x2 + 54y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9xy + x2 + 18y2) = 0 Factor a trinomial. 3((x + -6y)(x + -3y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -6y)' equal to zero and attempt to solve: Simplifying x + -6y = 0 Solving x + -6y = 0 Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. x + -6y + 6y = 0 + 6y Combine like terms: -6y + 6y = 0 x + 0 = 0 + 6y x = 0 + 6y Remove the zero: x = 6y Simplifying x = 6ySubproblem 2
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySolution
x = {6y, 3y}
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