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Simplifying 6a + 3b + -4c + -2a + 8a + 12b + -1b + 6c = 0 Reorder the terms: 6a + -2a + 8a + 3b + 12b + -1b + -4c + 6c = 0 Combine like terms: 6a + -2a = 4a 4a + 8a + 3b + 12b + -1b + -4c + 6c = 0 Combine like terms: 4a + 8a = 12a 12a + 3b + 12b + -1b + -4c + 6c = 0 Combine like terms: 3b + 12b = 15b 12a + 15b + -1b + -4c + 6c = 0 Combine like terms: 15b + -1b = 14b 12a + 14b + -4c + 6c = 0 Combine like terms: -4c + 6c = 2c 12a + 14b + 2c = 0 Solving 12a + 14b + 2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14b' to each side of the equation. 12a + 14b + -14b + 2c = 0 + -14b Combine like terms: 14b + -14b = 0 12a + 0 + 2c = 0 + -14b 12a + 2c = 0 + -14b Remove the zero: 12a + 2c = -14b Add '-2c' to each side of the equation. 12a + 2c + -2c = -14b + -2c Combine like terms: 2c + -2c = 0 12a + 0 = -14b + -2c 12a = -14b + -2c Divide each side by '12'. a = -1.166666667b + -0.1666666667c Simplifying a = -1.166666667b + -0.1666666667c
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