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Simplifying 12a + 14b + 2c + 4c + -6b + -5a = 0 Reorder the terms: 12a + -5a + 14b + -6b + 2c + 4c = 0 Combine like terms: 12a + -5a = 7a 7a + 14b + -6b + 2c + 4c = 0 Combine like terms: 14b + -6b = 8b 7a + 8b + 2c + 4c = 0 Combine like terms: 2c + 4c = 6c 7a + 8b + 6c = 0 Solving 7a + 8b + 6c = 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. 7a + 8b + -8b + 6c = 0 + -8b Combine like terms: 8b + -8b = 0 7a + 0 + 6c = 0 + -8b 7a + 6c = 0 + -8b Remove the zero: 7a + 6c = -8b Add '-6c' to each side of the equation. 7a + 6c + -6c = -8b + -6c Combine like terms: 6c + -6c = 0 7a + 0 = -8b + -6c 7a = -8b + -6c Divide each side by '7'. a = -1.142857143b + -0.8571428571c Simplifying a = -1.142857143b + -0.8571428571c
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