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Simplifying 9x2 + -57xy + -42y2 = 0 Reorder the terms: -57xy + 9x2 + -42y2 = 0 Solving -57xy + 9x2 + -42y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19xy + 3x2 + -14y2) = 0 Factor a trinomial. 3((x + -7y)(3x + 2y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -7y)' equal to zero and attempt to solve: Simplifying x + -7y = 0 Solving x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 x + 0 = 0 + 7y x = 0 + 7y Remove the zero: x = 7y Simplifying x = 7ySubproblem 2
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySolution
x = {7y, -0.6666666667y}
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