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Simplifying (a + -1b)(b + -1c)(c + -1a) = 0 Reorder the terms: (a + -1b)(b + -1c)(-1a + c) = 0 Multiply (a + -1b) * (b + -1c) (a(b + -1c) + -1b * (b + -1c))(-1a + c) = 0 ((b * a + -1c * a) + -1b * (b + -1c))(-1a + c) = 0 ((ab + -1ac) + -1b * (b + -1c))(-1a + c) = 0 (ab + -1ac + (b * -1b + -1c * -1b))(-1a + c) = 0 Reorder the terms: (ab + -1ac + (1bc + -1b2))(-1a + c) = 0 (ab + -1ac + (1bc + -1b2))(-1a + c) = 0 (ab + -1ac + 1bc + -1b2)(-1a + c) = 0 Multiply (ab + -1ac + 1bc + -1b2) * (-1a + c) (ab(-1a + c) + -1ac * (-1a + c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 ((-1a * ab + c * ab) + -1ac * (-1a + c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 Reorder the terms: ((abc + -1a2b) + -1ac * (-1a + c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 ((abc + -1a2b) + -1ac * (-1a + c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 (abc + -1a2b + (-1a * -1ac + c * -1ac) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 Reorder the terms: (abc + -1a2b + (-1ac2 + 1a2c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 (abc + -1a2b + (-1ac2 + 1a2c) + 1bc * (-1a + c) + -1b2 * (-1a + c)) = 0 (abc + -1a2b + -1ac2 + 1a2c + (-1a * 1bc + c * 1bc) + -1b2 * (-1a + c)) = 0 (abc + -1a2b + -1ac2 + 1a2c + (-1abc + 1bc2) + -1b2 * (-1a + c)) = 0 (abc + -1a2b + -1ac2 + 1a2c + -1abc + 1bc2 + (-1a * -1b2 + c * -1b2)) = 0 (abc + -1a2b + -1ac2 + 1a2c + -1abc + 1bc2 + (1ab2 + -1b2c)) = 0 Reorder the terms: (abc + -1abc + 1ab2 + -1ac2 + -1a2b + 1a2c + 1bc2 + -1b2c) = 0 Combine like terms: abc + -1abc = 0 (0 + 1ab2 + -1ac2 + -1a2b + 1a2c + 1bc2 + -1b2c) = 0 (1ab2 + -1ac2 + -1a2b + 1a2c + 1bc2 + -1b2c) = 0 Solving 1ab2 + -1ac2 + -1a2b + 1a2c + 1bc2 + -1b2c = 0 Solving for variable 'a'. The solution to this equation could not be determined.
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