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Simplifying (6a + 3b + 2c) + (5a + -2b + -1c) = 0 Remove parenthesis around (6a + 3b + 2c) 6a + 3b + 2c + (5a + -2b + -1c) = 0 Remove parenthesis around (5a + -2b + -1c) 6a + 3b + 2c + 5a + -2b + -1c = 0 Reorder the terms: 6a + 5a + 3b + -2b + 2c + -1c = 0 Combine like terms: 6a + 5a = 11a 11a + 3b + -2b + 2c + -1c = 0 Combine like terms: 3b + -2b = 1b 11a + 1b + 2c + -1c = 0 Combine like terms: 2c + -1c = 1c 11a + 1b + 1c = 0 Solving 11a + 1b + 1c = 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. 11a + 1b + -1b + 1c = 0 + -1b Combine like terms: 1b + -1b = 0 11a + 0 + 1c = 0 + -1b 11a + 1c = 0 + -1b Remove the zero: 11a + 1c = -1b Add '-1c' to each side of the equation. 11a + 1c + -1c = -1b + -1c Combine like terms: 1c + -1c = 0 11a + 0 = -1b + -1c 11a = -1b + -1c Divide each side by '11'. a = -0.09090909091b + -0.09090909091c Simplifying a = -0.09090909091b + -0.09090909091c
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