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Simplifying (x + -1y)(x + -2y) = 0 Multiply (x + -1y) * (x + -2y) (x(x + -2y) + -1y * (x + -2y)) = 0 ((x * x + -2y * x) + -1y * (x + -2y)) = 0 Reorder the terms: ((-2xy + x2) + -1y * (x + -2y)) = 0 ((-2xy + x2) + -1y * (x + -2y)) = 0 (-2xy + x2 + (x * -1y + -2y * -1y)) = 0 (-2xy + x2 + (-1xy + 2y2)) = 0 Reorder the terms: (-2xy + -1xy + x2 + 2y2) = 0 Combine like terms: -2xy + -1xy = -3xy (-3xy + x2 + 2y2) = 0 Solving -3xy + x2 + 2y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -2y)(x + -1y) = 0Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySolution
x = {2y, y}
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