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Simplifying 12x2 + -60xy + 75y2 = 0 Reorder the terms: -60xy + 12x2 + 75y2 = 0 Solving -60xy + 12x2 + 75y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-20xy + 4x2 + 25y2) = 0 Factor a trinomial. 3((2x + -5y)(2x + -5y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySubproblem 2
Set the factor '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySolution
x = {2.5y, 2.5y}
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