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Simplifying 10x2 + -24xy + -18y2 = 0 Reorder the terms: -24xy + 10x2 + -18y2 = 0 Solving -24xy + 10x2 + -18y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12xy + 5x2 + -9y2) = 0 Factor a trinomial. 2((x + -3y)(5x + 3y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySubproblem 2
Set the factor '(5x + 3y)' equal to zero and attempt to solve: Simplifying 5x + 3y = 0 Solving 5x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 5x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 5x + 0 = 0 + -3y 5x = 0 + -3y Remove the zero: 5x = -3y Divide each side by '5'. x = -0.6y Simplifying x = -0.6ySolution
x = {3y, -0.6y}
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