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Simplifying 6a + b + 3c + b + 3a + 3c = 0 Reorder the terms: 6a + 3a + b + b + 3c + 3c = 0 Combine like terms: 6a + 3a = 9a 9a + b + b + 3c + 3c = 0 Combine like terms: b + b = 2b 9a + 2b + 3c + 3c = 0 Combine like terms: 3c + 3c = 6c 9a + 2b + 6c = 0 Solving 9a + 2b + 6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 9a + 2b + -2b + 6c = 0 + -2b Combine like terms: 2b + -2b = 0 9a + 0 + 6c = 0 + -2b 9a + 6c = 0 + -2b Remove the zero: 9a + 6c = -2b Add '-6c' to each side of the equation. 9a + 6c + -6c = -2b + -6c Combine like terms: 6c + -6c = 0 9a + 0 = -2b + -6c 9a = -2b + -6c Divide each side by '9'. a = -0.2222222222b + -0.6666666667c Simplifying a = -0.2222222222b + -0.6666666667c
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