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Simplifying (2x + -1y)(x + -2y) = 0 Multiply (2x + -1y) * (x + -2y) (2x * (x + -2y) + -1y * (x + -2y)) = 0 ((x * 2x + -2y * 2x) + -1y * (x + -2y)) = 0 Reorder the terms: ((-4xy + 2x2) + -1y * (x + -2y)) = 0 ((-4xy + 2x2) + -1y * (x + -2y)) = 0 (-4xy + 2x2 + (x * -1y + -2y * -1y)) = 0 (-4xy + 2x2 + (-1xy + 2y2)) = 0 Reorder the terms: (-4xy + -1xy + 2x2 + 2y2) = 0 Combine like terms: -4xy + -1xy = -5xy (-5xy + 2x2 + 2y2) = 0 Solving -5xy + 2x2 + 2y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -2y)(2x + -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 '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySolution
x = {2y, 0.5y}
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