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