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Simplifying 6x2 + -5xy + -6y2 = 0 Reorder the terms: -5xy + 6x2 + -6y2 = 0 Solving -5xy + 6x2 + -6y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -3y)(3x + 2y) = 0Subproblem 1
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 = 1.5ySubproblem 2
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySolution
x = {1.5y, -0.6666666667y}
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