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Simplifying (4a + 3b + -1c) + (5a + -1c + b) + (4b + -6a) = 0 Remove parenthesis around (4a + 3b + -1c) 4a + 3b + -1c + (5a + -1c + b) + (4b + -6a) = 0 Reorder the terms: 4a + 3b + -1c + (5a + b + -1c) + (4b + -6a) = 0 Remove parenthesis around (5a + b + -1c) 4a + 3b + -1c + 5a + b + -1c + (4b + -6a) = 0 Reorder the terms: 4a + 3b + -1c + 5a + b + -1c + (-6a + 4b) = 0 Remove parenthesis around (-6a + 4b) 4a + 3b + -1c + 5a + b + -1c + -6a + 4b = 0 Reorder the terms: 4a + 5a + -6a + 3b + b + 4b + -1c + -1c = 0 Combine like terms: 4a + 5a = 9a 9a + -6a + 3b + b + 4b + -1c + -1c = 0 Combine like terms: 9a + -6a = 3a 3a + 3b + b + 4b + -1c + -1c = 0 Combine like terms: 3b + b = 4b 3a + 4b + 4b + -1c + -1c = 0 Combine like terms: 4b + 4b = 8b 3a + 8b + -1c + -1c = 0 Combine like terms: -1c + -1c = -2c 3a + 8b + -2c = 0 Solving 3a + 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. 3a + 8b + -8b + -2c = 0 + -8b Combine like terms: 8b + -8b = 0 3a + 0 + -2c = 0 + -8b 3a + -2c = 0 + -8b Remove the zero: 3a + -2c = -8b Add '2c' to each side of the equation. 3a + -2c + 2c = -8b + 2c Combine like terms: -2c + 2c = 0 3a + 0 = -8b + 2c 3a = -8b + 2c Divide each side by '3'. a = -2.666666667b + 0.6666666667c Simplifying a = -2.666666667b + 0.6666666667c
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