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Simplifying (8y + -2x)(2y + -4x) = 0 Reorder the terms: (-2x + 8y)(2y + -4x) = 0 Reorder the terms: (-2x + 8y)(-4x + 2y) = 0 Multiply (-2x + 8y) * (-4x + 2y) (-2x * (-4x + 2y) + 8y * (-4x + 2y)) = 0 ((-4x * -2x + 2y * -2x) + 8y * (-4x + 2y)) = 0 Reorder the terms: ((-4xy + 8x2) + 8y * (-4x + 2y)) = 0 ((-4xy + 8x2) + 8y * (-4x + 2y)) = 0 (-4xy + 8x2 + (-4x * 8y + 2y * 8y)) = 0 (-4xy + 8x2 + (-32xy + 16y2)) = 0 Reorder the terms: (-4xy + -32xy + 8x2 + 16y2) = 0 Combine like terms: -4xy + -32xy = -36xy (-36xy + 8x2 + 16y2) = 0 Solving -36xy + 8x2 + 16y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9xy + 2x2 + 4y2) = 0 Factor a trinomial. 4((x + -4y)(2x + -1y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4ySubproblem 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 = {4y, 0.5y}
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