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Simplifying 6x2 + 78xy + 180y2 = 0 Reorder the terms: 78xy + 6x2 + 180y2 = 0 Solving 78xy + 6x2 + 180y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(13xy + x2 + 30y2) = 0 Factor a trinomial. 6((x + 3y)(x + 10y)) = 0 Ignore the factor 6.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 '(x + 10y)' equal to zero and attempt to solve: Simplifying x + 10y = 0 Solving x + 10y = 0 Move all terms containing x to the left, all other terms to the right. Add '-10y' to each side of the equation. x + 10y + -10y = 0 + -10y Combine like terms: 10y + -10y = 0 x + 0 = 0 + -10y x = 0 + -10y Remove the zero: x = -10y Simplifying x = -10ySolution
x = {-3y, -10y}
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