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Simplifying 6x2 + -27xy + -15y2 = 0 Reorder the terms: -27xy + 6x2 + -15y2 = 0 Solving -27xy + 6x2 + -15y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9xy + 2x2 + -5y2) = 0 Factor a trinomial. 3((x + -5y)(2x + y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySubproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {5y, -0.5y}
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