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Simplifying 12x2 + -27xy + -27y2 = 0 Reorder the terms: -27xy + 12x2 + -27y2 = 0 Solving -27xy + 12x2 + -27y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9xy + 4x2 + -9y2) = 0 Factor a trinomial. 3((x + -3y)(4x + 3y)) = 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 '(4x + 3y)' equal to zero and attempt to solve: Simplifying 4x + 3y = 0 Solving 4x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 4x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 4x + 0 = 0 + -3y 4x = 0 + -3y Remove the zero: 4x = -3y Divide each side by '4'. x = -0.75y Simplifying x = -0.75ySolution
x = {3y, -0.75y}
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