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Simplifying 12a + 14b + 2c + 2c + -6b + -3a = 0 Reorder the terms: 12a + -3a + 14b + -6b + 2c + 2c = 0 Combine like terms: 12a + -3a = 9a 9a + 14b + -6b + 2c + 2c = 0 Combine like terms: 14b + -6b = 8b 9a + 8b + 2c + 2c = 0 Combine like terms: 2c + 2c = 4c 9a + 8b + 4c = 0 Solving 9a + 8b + 4c = 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. 9a + 8b + -8b + 4c = 0 + -8b Combine like terms: 8b + -8b = 0 9a + 0 + 4c = 0 + -8b 9a + 4c = 0 + -8b Remove the zero: 9a + 4c = -8b Add '-4c' to each side of the equation. 9a + 4c + -4c = -8b + -4c Combine like terms: 4c + -4c = 0 9a + 0 = -8b + -4c 9a = -8b + -4c Divide each side by '9'. a = -0.8888888889b + -0.4444444444c Simplifying a = -0.8888888889b + -0.4444444444c
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