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Simplifying y(x + y)(2x + 2y) = 0 Multiply (x + y) * (2x + 2y) y(x(2x + 2y) + y(2x + 2y)) = 0 y((2x * x + 2y * x) + y(2x + 2y)) = 0 Reorder the terms: y((2xy + 2x2) + y(2x + 2y)) = 0 y((2xy + 2x2) + y(2x + 2y)) = 0 y(2xy + 2x2 + (2x * y + 2y * y)) = 0 y(2xy + 2x2 + (2xy + 2y2)) = 0 Reorder the terms: y(2xy + 2xy + 2x2 + 2y2) = 0 Combine like terms: 2xy + 2xy = 4xy y(4xy + 2x2 + 2y2) = 0 (4xy * y + 2x2 * y + 2y2 * y) = 0 (4xy2 + 2x2y + 2y3) = 0 Solving 4xy2 + 2x2y + 2y3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(2xy + x2 + y2) = 0 Factor a trinomial. 2y((x + y)(x + y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying 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 '(x + y)' equal to zero and attempt to solve: Simplifying 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 = -1ySolution
x = {-1y, -1y}
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