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Simplifying 3y(x + y) * 4x(x + -1y) = 0 Reorder the terms for easier multiplication: 3 * 4y * x(x + y)(x + -1y) = 0 Multiply 3 * 4 12y * x(x + y)(x + -1y) = 0 Multiply y * x 12xy(x + y)(x + -1y) = 0 Multiply (x + y) * (x + -1y) 12xy(x(x + -1y) + y(x + -1y)) = 0 12xy((x * x + -1y * x) + y(x + -1y)) = 0 Reorder the terms: 12xy((-1xy + x2) + y(x + -1y)) = 0 12xy((-1xy + x2) + y(x + -1y)) = 0 12xy(-1xy + x2 + (x * y + -1y * y)) = 0 12xy(-1xy + x2 + (xy + -1y2)) = 0 Reorder the terms: 12xy(-1xy + xy + x2 + -1y2) = 0 Combine like terms: -1xy + xy = 0 12xy(0 + x2 + -1y2) = 0 12xy(x2 + -1y2) = 0 (x2 * 12xy + -1y2 * 12xy) = 0 Reorder the terms: (-12xy3 + 12x3y) = 0 (-12xy3 + 12x3y) = 0 Solving -12xy3 + 12x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12xy'. 12xy(-1y2 + x2) = 0 Factor a difference between two squares. 12xy((y + x)(-1y + x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 0 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 '(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 = {-1y, y}
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