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Simplifying 12x2 + 21xy + -45y2 = 0 Reorder the terms: 21xy + 12x2 + -45y2 = 0 Solving 21xy + 12x2 + -45y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(7xy + 4x2 + -15y2) = 0 Factor a trinomial. 3((4x + -5y)(x + 3y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve: Simplifying 4x + -5y = 0 Solving 4x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 4x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 4x + 0 = 0 + 5y 4x = 0 + 5y Remove the zero: 4x = 5y Divide each side by '4'. x = 1.25y Simplifying x = 1.25ySubproblem 2
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 = -3ySolution
x = {1.25y, -3y}
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