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Simplifying 12a + 11b + 4c + 5c + -3b + -6a = 0 Reorder the terms: 12a + -6a + 11b + -3b + 4c + 5c = 0 Combine like terms: 12a + -6a = 6a 6a + 11b + -3b + 4c + 5c = 0 Combine like terms: 11b + -3b = 8b 6a + 8b + 4c + 5c = 0 Combine like terms: 4c + 5c = 9c 6a + 8b + 9c = 0 Solving 6a + 8b + 9c = 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. 6a + 8b + -8b + 9c = 0 + -8b Combine like terms: 8b + -8b = 0 6a + 0 + 9c = 0 + -8b 6a + 9c = 0 + -8b Remove the zero: 6a + 9c = -8b Add '-9c' to each side of the equation. 6a + 9c + -9c = -8b + -9c Combine like terms: 9c + -9c = 0 6a + 0 = -8b + -9c 6a = -8b + -9c Divide each side by '6'. a = -1.333333333b + -1.5c Simplifying a = -1.333333333b + -1.5c
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