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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 + 3y)(x + 6y)) = 0 Ignore the factor 3.Subproblem 1
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 = -3ySubproblem 2
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 = -6ySolution
x = {-3y, -6y}
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