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Simplifying (2xy + -1x)(2xy + x) = 0 Reorder the terms: (-1x + 2xy)(2xy + x) = 0 Reorder the terms: (-1x + 2xy)(x + 2xy) = 0 Multiply (-1x + 2xy) * (x + 2xy) (-1x * (x + 2xy) + 2xy * (x + 2xy)) = 0 ((x * -1x + 2xy * -1x) + 2xy * (x + 2xy)) = 0 ((-1x2 + -2x2y) + 2xy * (x + 2xy)) = 0 (-1x2 + -2x2y + (x * 2xy + 2xy * 2xy)) = 0 (-1x2 + -2x2y + (2x2y + 4x2y2)) = 0 Combine like terms: -2x2y + 2x2y = 0 (-1x2 + 0 + 4x2y2) = 0 (-1x2 + 4x2y2) = 0 Solving -1x2 + 4x2y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + 4y2) = 0 Factor a difference between two squares. x2((1 + 2y)(-1 + 2y)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Add '-2y' to each side of the equation. 2y + -2y = -1 + -2y Combine like terms: 2y + -2y = 0 0 = -1 + -2y Simplifying 0 = -1 + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1 + 2y)' equal to zero and attempt to solve: Simplifying -1 + 2y = 0 Solving -1 + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2y = 0 + 1 2y = 0 + 1 Combine like terms: 0 + 1 = 1 2y = 1 Add '-2y' to each side of the equation. 2y + -2y = 1 + -2y Combine like terms: 2y + -2y = 0 0 = 1 + -2y Simplifying 0 = 1 + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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