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