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Simplifying 12x2 + -2xy + -30y2 = 0 Reorder the terms: -2xy + 12x2 + -30y2 = 0 Solving -2xy + 12x2 + -30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1xy + 6x2 + -15y2) = 0 Factor a trinomial. 2((3x + -5y)(2x + 3y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3x + -5y)' equal to zero and attempt to solve: Simplifying 3x + -5y = 0 Solving 3x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 3x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 3x + 0 = 0 + 5y 3x = 0 + 5y Remove the zero: 3x = 5y Divide each side by '3'. x = 1.666666667y Simplifying x = 1.666666667ySubproblem 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 = {1.666666667y, -1.5y}
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