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Simplifying 15x2 + -153xy + 162y2 = 0 Reorder the terms: -153xy + 15x2 + 162y2 = 0 Solving -153xy + 15x2 + 162y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-51xy + 5x2 + 54y2) = 0 Factor a trinomial. 3((x + -9y)(5x + -6y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -9y)' equal to zero and attempt to solve: Simplifying x + -9y = 0 Solving x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 x + 0 = 0 + 9y x = 0 + 9y Remove the zero: x = 9y Simplifying x = 9ySubproblem 2
Set the factor '(5x + -6y)' equal to zero and attempt to solve: Simplifying 5x + -6y = 0 Solving 5x + -6y = 0 Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. 5x + -6y + 6y = 0 + 6y Combine like terms: -6y + 6y = 0 5x + 0 = 0 + 6y 5x = 0 + 6y Remove the zero: 5x = 6y Divide each side by '5'. x = 1.2y Simplifying x = 1.2ySolution
x = {9y, 1.2y}
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