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Simplifying 12x2 + 8xy + -15y2 = 0 Reorder the terms: 8xy + 12x2 + -15y2 = 0 Solving 8xy + 12x2 + -15y2 = 0 Solving for variable 'x'. Factor a trinomial. (6x + -5y)(2x + 3y) = 0Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve: Simplifying 6x + -5y = 0 Solving 6x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 6x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 6x + 0 = 0 + 5y 6x = 0 + 5y Remove the zero: 6x = 5y Divide each side by '6'. x = 0.8333333333y Simplifying x = 0.8333333333ySubproblem 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 = {0.8333333333y, -1.5y}
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