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Simplifying (6x + -1y)(x + -3y) = 0 Multiply (6x + -1y) * (x + -3y) (6x * (x + -3y) + -1y * (x + -3y)) = 0 ((x * 6x + -3y * 6x) + -1y * (x + -3y)) = 0 Reorder the terms: ((-18xy + 6x2) + -1y * (x + -3y)) = 0 ((-18xy + 6x2) + -1y * (x + -3y)) = 0 (-18xy + 6x2 + (x * -1y + -3y * -1y)) = 0 (-18xy + 6x2 + (-1xy + 3y2)) = 0 Reorder the terms: (-18xy + -1xy + 6x2 + 3y2) = 0 Combine like terms: -18xy + -1xy = -19xy (-19xy + 6x2 + 3y2) = 0 Solving -19xy + 6x2 + 3y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -3y)(6x + -1y) = 0Subproblem 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 '(6x + -1y)' equal to zero and attempt to solve: Simplifying 6x + -1y = 0 Solving 6x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 6x + -1y + y = 0 + y Combine like terms: -1y + y = 0 6x + 0 = 0 + y 6x = 0 + y Remove the zero: 6x = y Divide each side by '6'. x = 0.1666666667y Simplifying x = 0.1666666667ySolution
x = {3y, 0.1666666667y}
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