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Simplifying 15x2 + -69xy + -30y2 = 0 Reorder the terms: -69xy + 15x2 + -30y2 = 0 Solving -69xy + 15x2 + -30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-23xy + 5x2 + -10y2) = 0 Factor a trinomial. 3((x + -5y)(5x + 2y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySubproblem 2
Set the factor '(5x + 2y)' equal to zero and attempt to solve: Simplifying 5x + 2y = 0 Solving 5x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 5x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 5x + 0 = 0 + -2y 5x = 0 + -2y Remove the zero: 5x = -2y Divide each side by '5'. x = -0.4y Simplifying x = -0.4ySolution
x = {5y, -0.4y}
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