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Simplifying 45y2 + -60xy + 20x2 = 0 Reorder the terms: -60xy + 20x2 + 45y2 = 0 Solving -60xy + 20x2 + 45y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-12xy + 4x2 + 9y2) = 0 Factor a trinomial. 5((2x + -3y)(2x + -3y)) = 0 Ignore the factor 5.Subproblem 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 '(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 = {1.5y, 1.5y}
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