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Simplifying (5x + y)(5x + y)(5x + y)(5x + y)(5x + y) = 0 Multiply (5x + y) * (5x + y) (5x * (5x + y) + y(5x + y))(5x + y)(5x + y)(5x + y) = 0 ((5x * 5x + y * 5x) + y(5x + y))(5x + y)(5x + y)(5x + y) = 0 Reorder the terms: ((5xy + 25x2) + y(5x + y))(5x + y)(5x + y)(5x + y) = 0 ((5xy + 25x2) + y(5x + y))(5x + y)(5x + y)(5x + y) = 0 (5xy + 25x2 + (5x * y + y * y))(5x + y)(5x + y)(5x + y) = 0 (5xy + 25x2 + (5xy + y2))(5x + y)(5x + y)(5x + y) = 0 Reorder the terms: (5xy + 5xy + 25x2 + y2)(5x + y)(5x + y)(5x + y) = 0 Combine like terms: 5xy + 5xy = 10xy (10xy + 25x2 + y2)(5x + y)(5x + y)(5x + y) = 0 Multiply (10xy + 25x2 + y2) * (5x + y) (10xy * (5x + y) + 25x2 * (5x + y) + y2(5x + y))(5x + y)(5x + y) = 0 ((5x * 10xy + y * 10xy) + 25x2 * (5x + y) + y2(5x + y))(5x + y)(5x + y) = 0 Reorder the terms: ((10xy2 + 50x2y) + 25x2 * (5x + y) + y2(5x + y))(5x + y)(5x + y) = 0 ((10xy2 + 50x2y) + 25x2 * (5x + y) + y2(5x + y))(5x + y)(5x + y) = 0 (10xy2 + 50x2y + (5x * 25x2 + y * 25x2) + y2(5x + y))(5x + y)(5x + y) = 0 Reorder the terms: (10xy2 + 50x2y + (25x2y + 125x3) + y2(5x + y))(5x + y)(5x + y) = 0 (10xy2 + 50x2y + (25x2y + 125x3) + y2(5x + y))(5x + y)(5x + y) = 0 (10xy2 + 50x2y + 25x2y + 125x3 + (5x * y2 + y * y2))(5x + y)(5x + y) = 0 (10xy2 + 50x2y + 25x2y + 125x3 + (5xy2 + y3))(5x + y)(5x + y) = 0 Reorder the terms: (10xy2 + 5xy2 + 50x2y + 25x2y + 125x3 + y3)(5x + y)(5x + y) = 0 Combine like terms: 10xy2 + 5xy2 = 15xy2 (15xy2 + 50x2y + 25x2y + 125x3 + y3)(5x + y)(5x + y) = 0 Combine like terms: 50x2y + 25x2y = 75x2y (15xy2 + 75x2y + 125x3 + y3)(5x + y)(5x + y) = 0 Multiply (15xy2 + 75x2y + 125x3 + y3) * (5x + y) (15xy2 * (5x + y) + 75x2y * (5x + y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 ((5x * 15xy2 + y * 15xy2) + 75x2y * (5x + y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 Reorder the terms: ((15xy3 + 75x2y2) + 75x2y * (5x + y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 ((15xy3 + 75x2y2) + 75x2y * (5x + y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 (15xy3 + 75x2y2 + (5x * 75x2y + y * 75x2y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 Reorder the terms: (15xy3 + 75x2y2 + (75x2y2 + 375x3y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 (15xy3 + 75x2y2 + (75x2y2 + 375x3y) + 125x3 * (5x + y) + y3(5x + y))(5x + y) = 0 (15xy3 + 75x2y2 + 75x2y2 + 375x3y + (5x * 125x3 + y * 125x3) + y3(5x + y))(5x + y) = 0 Reorder the terms: (15xy3 + 75x2y2 + 75x2y2 + 375x3y + (125x3y + 625x4) + y3(5x + y))(5x + y) = 0 (15xy3 + 75x2y2 + 75x2y2 + 375x3y + (125x3y + 625x4) + y3(5x + y))(5x + y) = 0 (15xy3 + 75x2y2 + 75x2y2 + 375x3y + 125x3y + 625x4 + (5x * y3 + y * y3))(5x + y) = 0 (15xy3 + 75x2y2 + 75x2y2 + 375x3y + 125x3y + 625x4 + (5xy3 + y4))(5x + y) = 0 Reorder the terms: (15xy3 + 5xy3 + 75x2y2 + 75x2y2 + 375x3y + 125x3y + 625x4 + y4)(5x + y) = 0 Combine like terms: 15xy3 + 5xy3 = 20xy3 (20xy3 + 75x2y2 + 75x2y2 + 375x3y + 125x3y + 625x4 + y4)(5x + y) = 0 Combine like terms: 75x2y2 + 75x2y2 = 150x2y2 (20xy3 + 150x2y2 + 375x3y + 125x3y + 625x4 + y4)(5x + y) = 0 Combine like terms: 375x3y + 125x3y = 500x3y (20xy3 + 150x2y2 + 500x3y + 625x4 + y4)(5x + y) = 0 Multiply (20xy3 + 150x2y2 + 500x3y + 625x4 + y4) * (5x + y) (20xy3 * (5x + y) + 150x2y2 * (5x + y) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 ((5x * 20xy3 + y * 20xy3) + 150x2y2 * (5x + y) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 Reorder the terms: ((20xy4 + 100x2y3) + 150x2y2 * (5x + y) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 ((20xy4 + 100x2y3) + 150x2y2 * (5x + y) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + (5x * 150x2y2 + y * 150x2y2) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 Reorder the terms: (20xy4 + 100x2y3 + (150x2y3 + 750x3y2) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + (150x2y3 + 750x3y2) + 500x3y * (5x + y) + 625x4 * (5x + y) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + (5x * 500x3y + y * 500x3y) + 625x4 * (5x + y) + y4(5x + y)) = 0 Reorder the terms: (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + (500x3y2 + 2500x4y) + 625x4 * (5x + y) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + (500x3y2 + 2500x4y) + 625x4 * (5x + y) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + (5x * 625x4 + y * 625x4) + y4(5x + y)) = 0 Reorder the terms: (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + (625x4y + 3125x5) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + (625x4y + 3125x5) + y4(5x + y)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + 625x4y + 3125x5 + (5x * y4 + y * y4)) = 0 (20xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + 625x4y + 3125x5 + (5xy4 + y5)) = 0 Reorder the terms: (20xy4 + 5xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + 625x4y + 3125x5 + y5) = 0 Combine like terms: 20xy4 + 5xy4 = 25xy4 (25xy4 + 100x2y3 + 150x2y3 + 750x3y2 + 500x3y2 + 2500x4y + 625x4y + 3125x5 + y5) = 0 Combine like terms: 100x2y3 + 150x2y3 = 250x2y3 (25xy4 + 250x2y3 + 750x3y2 + 500x3y2 + 2500x4y + 625x4y + 3125x5 + y5) = 0 Combine like terms: 750x3y2 + 500x3y2 = 1250x3y2 (25xy4 + 250x2y3 + 1250x3y2 + 2500x4y + 625x4y + 3125x5 + y5) = 0 Combine like terms: 2500x4y + 625x4y = 3125x4y (25xy4 + 250x2y3 + 1250x3y2 + 3125x4y + 3125x5 + y5) = 0 Solving 25xy4 + 250x2y3 + 1250x3y2 + 3125x4y + 3125x5 + y5 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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