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Simplifying 12a + 15b + 5c + 2c + -6a + -6b = 0 Reorder the terms: 12a + -6a + 15b + -6b + 5c + 2c = 0 Combine like terms: 12a + -6a = 6a 6a + 15b + -6b + 5c + 2c = 0 Combine like terms: 15b + -6b = 9b 6a + 9b + 5c + 2c = 0 Combine like terms: 5c + 2c = 7c 6a + 9b + 7c = 0 Solving 6a + 9b + 7c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 6a + 9b + -9b + 7c = 0 + -9b Combine like terms: 9b + -9b = 0 6a + 0 + 7c = 0 + -9b 6a + 7c = 0 + -9b Remove the zero: 6a + 7c = -9b Add '-7c' to each side of the equation. 6a + 7c + -7c = -9b + -7c Combine like terms: 7c + -7c = 0 6a + 0 = -9b + -7c 6a = -9b + -7c Divide each side by '6'. a = -1.5b + -1.166666667c Simplifying a = -1.5b + -1.166666667c
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