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Simplifying (3a + 4b + -5c) + (2a + -7b + -6c) + (8a + -5b + 9c) = 0 Remove parenthesis around (3a + 4b + -5c) 3a + 4b + -5c + (2a + -7b + -6c) + (8a + -5b + 9c) = 0 Remove parenthesis around (2a + -7b + -6c) 3a + 4b + -5c + 2a + -7b + -6c + (8a + -5b + 9c) = 0 Remove parenthesis around (8a + -5b + 9c) 3a + 4b + -5c + 2a + -7b + -6c + 8a + -5b + 9c = 0 Reorder the terms: 3a + 2a + 8a + 4b + -7b + -5b + -5c + -6c + 9c = 0 Combine like terms: 3a + 2a = 5a 5a + 8a + 4b + -7b + -5b + -5c + -6c + 9c = 0 Combine like terms: 5a + 8a = 13a 13a + 4b + -7b + -5b + -5c + -6c + 9c = 0 Combine like terms: 4b + -7b = -3b 13a + -3b + -5b + -5c + -6c + 9c = 0 Combine like terms: -3b + -5b = -8b 13a + -8b + -5c + -6c + 9c = 0 Combine like terms: -5c + -6c = -11c 13a + -8b + -11c + 9c = 0 Combine like terms: -11c + 9c = -2c 13a + -8b + -2c = 0 Solving 13a + -8b + -2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8b' to each side of the equation. 13a + -8b + 8b + -2c = 0 + 8b Combine like terms: -8b + 8b = 0 13a + 0 + -2c = 0 + 8b 13a + -2c = 0 + 8b Remove the zero: 13a + -2c = 8b Add '2c' to each side of the equation. 13a + -2c + 2c = 8b + 2c Combine like terms: -2c + 2c = 0 13a + 0 = 8b + 2c 13a = 8b + 2c Divide each side by '13'. a = 0.6153846154b + 0.1538461538c Simplifying a = 0.6153846154b + 0.1538461538c
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