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Simplifying 15x2 + 18xy + -20xy + -24y2 = 0 Reorder the terms: 18xy + -20xy + 15x2 + -24y2 = 0 Combine like terms: 18xy + -20xy = -2xy -2xy + 15x2 + -24y2 = 0 Solving -2xy + 15x2 + -24y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -4y)(5x + 6y) = 0Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333ySubproblem 2
Set the factor '(5x + 6y)' equal to zero and attempt to solve: Simplifying 5x + 6y = 0 Solving 5x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. 5x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 5x + 0 = 0 + -6y 5x = 0 + -6y Remove the zero: 5x = -6y Divide each side by '5'. x = -1.2y Simplifying x = -1.2ySolution
x = {1.333333333y, -1.2y}
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