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Simplifying 12a + 19b + 6c + 2c + -2b + -2a = 0 Reorder the terms: 12a + -2a + 19b + -2b + 6c + 2c = 0 Combine like terms: 12a + -2a = 10a 10a + 19b + -2b + 6c + 2c = 0 Combine like terms: 19b + -2b = 17b 10a + 17b + 6c + 2c = 0 Combine like terms: 6c + 2c = 8c 10a + 17b + 8c = 0 Solving 10a + 17b + 8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-17b' to each side of the equation. 10a + 17b + -17b + 8c = 0 + -17b Combine like terms: 17b + -17b = 0 10a + 0 + 8c = 0 + -17b 10a + 8c = 0 + -17b Remove the zero: 10a + 8c = -17b Add '-8c' to each side of the equation. 10a + 8c + -8c = -17b + -8c Combine like terms: 8c + -8c = 0 10a + 0 = -17b + -8c 10a = -17b + -8c Divide each side by '10'. a = -1.7b + -0.8c Simplifying a = -1.7b + -0.8c
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