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Simplifying 2x(x2 + -1xy + yx + -1y2) = 0 Reorder the terms: 2x(-1xy + xy + x2 + -1y2) = 0 Combine like terms: -1xy + xy = 0 2x(0 + x2 + -1y2) = 0 2x(x2 + -1y2) = 0 (x2 * 2x + -1y2 * 2x) = 0 Reorder the terms: (-2xy2 + 2x3) = 0 (-2xy2 + 2x3) = 0 Solving -2xy2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1y2 + x2) = 0 Factor a difference between two squares. 2x((y + x)(-1y + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySubproblem 3
Set the factor '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: 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 = {0, -1y, y}
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