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