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Simplifying (a + b + c) + (a + b + 2c) + (a + b + c) = 0 Remove parenthesis around (a + b + c) a + b + c + (a + b + 2c) + (a + b + c) = 0 Remove parenthesis around (a + b + 2c) a + b + c + a + b + 2c + (a + b + c) = 0 Remove parenthesis around (a + b + c) a + b + c + a + b + 2c + a + b + c = 0 Reorder the terms: a + a + a + b + b + b + c + 2c + c = 0 Combine like terms: a + a = 2a 2a + a + b + b + b + c + 2c + c = 0 Combine like terms: 2a + a = 3a 3a + b + b + b + c + 2c + c = 0 Combine like terms: b + b = 2b 3a + 2b + b + c + 2c + c = 0 Combine like terms: 2b + b = 3b 3a + 3b + c + 2c + c = 0 Combine like terms: c + 2c = 3c 3a + 3b + 3c + c = 0 Combine like terms: 3c + c = 4c 3a + 3b + 4c = 0 Solving 3a + 3b + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 3a + 3b + -3b + 4c = 0 + -3b Combine like terms: 3b + -3b = 0 3a + 0 + 4c = 0 + -3b 3a + 4c = 0 + -3b Remove the zero: 3a + 4c = -3b Add '-4c' to each side of the equation. 3a + 4c + -4c = -3b + -4c Combine like terms: 4c + -4c = 0 3a + 0 = -3b + -4c 3a = -3b + -4c Divide each side by '3'. a = -1b + -1.333333333c Simplifying a = -1b + -1.333333333c
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