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Simplifying 12a + 15b + 4c + 5c + -5b + -6a = 0 Reorder the terms: 12a + -6a + 15b + -5b + 4c + 5c = 0 Combine like terms: 12a + -6a = 6a 6a + 15b + -5b + 4c + 5c = 0 Combine like terms: 15b + -5b = 10b 6a + 10b + 4c + 5c = 0 Combine like terms: 4c + 5c = 9c 6a + 10b + 9c = 0 Solving 6a + 10b + 9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. 6a + 10b + -10b + 9c = 0 + -10b Combine like terms: 10b + -10b = 0 6a + 0 + 9c = 0 + -10b 6a + 9c = 0 + -10b Remove the zero: 6a + 9c = -10b Add '-9c' to each side of the equation. 6a + 9c + -9c = -10b + -9c Combine like terms: 9c + -9c = 0 6a + 0 = -10b + -9c 6a = -10b + -9c Divide each side by '6'. a = -1.666666667b + -1.5c Simplifying a = -1.666666667b + -1.5c
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