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Simplifying 12a + 20b + 6c + 3c + -3b + -4a = 0 Reorder the terms: 12a + -4a + 20b + -3b + 6c + 3c = 0 Combine like terms: 12a + -4a = 8a 8a + 20b + -3b + 6c + 3c = 0 Combine like terms: 20b + -3b = 17b 8a + 17b + 6c + 3c = 0 Combine like terms: 6c + 3c = 9c 8a + 17b + 9c = 0 Solving 8a + 17b + 9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-17b' to each side of the equation. 8a + 17b + -17b + 9c = 0 + -17b Combine like terms: 17b + -17b = 0 8a + 0 + 9c = 0 + -17b 8a + 9c = 0 + -17b Remove the zero: 8a + 9c = -17b Add '-9c' to each side of the equation. 8a + 9c + -9c = -17b + -9c Combine like terms: 9c + -9c = 0 8a + 0 = -17b + -9c 8a = -17b + -9c Divide each side by '8'. a = -2.125b + -1.125c Simplifying a = -2.125b + -1.125c
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