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Simplifying (a + b + -1c)(a + b + c) = 0 Multiply (a + b + -1c) * (a + b + c) (a(a + b + c) + b(a + b + c) + -1c * (a + b + c)) = 0 ((a * a + b * a + c * a) + b(a + b + c) + -1c * (a + b + c)) = 0 Reorder the terms: ((ab + ac + a2) + b(a + b + c) + -1c * (a + b + c)) = 0 ((ab + ac + a2) + b(a + b + c) + -1c * (a + b + c)) = 0 (ab + ac + a2 + (a * b + b * b + c * b) + -1c * (a + b + c)) = 0 Reorder the terms: (ab + ac + a2 + (ab + bc + b2) + -1c * (a + b + c)) = 0 (ab + ac + a2 + (ab + bc + b2) + -1c * (a + b + c)) = 0 (ab + ac + a2 + ab + bc + b2 + (a * -1c + b * -1c + c * -1c)) = 0 (ab + ac + a2 + ab + bc + b2 + (-1ac + -1bc + -1c2)) = 0 Reorder the terms: (ab + ab + ac + -1ac + a2 + bc + -1bc + b2 + -1c2) = 0 Combine like terms: ab + ab = 2ab (2ab + ac + -1ac + a2 + bc + -1bc + b2 + -1c2) = 0 Combine like terms: ac + -1ac = 0 (2ab + 0 + a2 + bc + -1bc + b2 + -1c2) = 0 (2ab + a2 + bc + -1bc + b2 + -1c2) = 0 Combine like terms: bc + -1bc = 0 (2ab + a2 + 0 + b2 + -1c2) = 0 (2ab + a2 + b2 + -1c2) = 0 Solving 2ab + a2 + b2 + -1c2 = 0 Solving for variable 'a'. The solution to this equation could not be determined.
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