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Simplifying 12a + 14b + 5c + 5c + -3b + -5a = 0 Reorder the terms: 12a + -5a + 14b + -3b + 5c + 5c = 0 Combine like terms: 12a + -5a = 7a 7a + 14b + -3b + 5c + 5c = 0 Combine like terms: 14b + -3b = 11b 7a + 11b + 5c + 5c = 0 Combine like terms: 5c + 5c = 10c 7a + 11b + 10c = 0 Solving 7a + 11b + 10c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11b' to each side of the equation. 7a + 11b + -11b + 10c = 0 + -11b Combine like terms: 11b + -11b = 0 7a + 0 + 10c = 0 + -11b 7a + 10c = 0 + -11b Remove the zero: 7a + 10c = -11b Add '-10c' to each side of the equation. 7a + 10c + -10c = -11b + -10c Combine like terms: 10c + -10c = 0 7a + 0 = -11b + -10c 7a = -11b + -10c Divide each side by '7'. a = -1.571428571b + -1.428571429c Simplifying a = -1.571428571b + -1.428571429c
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