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Simplifying 2x2 + -6xy + 3xy + -9y2 = 0 Reorder the terms: -6xy + 3xy + 2x2 + -9y2 = 0 Combine like terms: -6xy + 3xy = -3xy -3xy + 2x2 + -9y2 = 0 Solving -3xy + 2x2 + -9y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -3y)(2x + 3y) = 0Subproblem 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 '(2x + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 2x + 0 = 0 + -3y 2x = 0 + -3y Remove the zero: 2x = -3y Divide each side by '2'. x = -1.5y Simplifying x = -1.5ySolution
x = {3y, -1.5y}
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