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Simplifying 12a + 16b + 2c + 4c + -4b + -6a = 0 Reorder the terms: 12a + -6a + 16b + -4b + 2c + 4c = 0 Combine like terms: 12a + -6a = 6a 6a + 16b + -4b + 2c + 4c = 0 Combine like terms: 16b + -4b = 12b 6a + 12b + 2c + 4c = 0 Combine like terms: 2c + 4c = 6c 6a + 12b + 6c = 0 Solving 6a + 12b + 6c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12b' to each side of the equation. 6a + 12b + -12b + 6c = 0 + -12b Combine like terms: 12b + -12b = 0 6a + 0 + 6c = 0 + -12b 6a + 6c = 0 + -12b Remove the zero: 6a + 6c = -12b Add '-6c' to each side of the equation. 6a + 6c + -6c = -12b + -6c Combine like terms: 6c + -6c = 0 6a + 0 = -12b + -6c 6a = -12b + -6c Divide each side by '6'. a = -2b + -1c Simplifying a = -2b + -1c
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