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Simplifying 12a + 20b + 3c + 4c + -3b + -3a = 0 Reorder the terms: 12a + -3a + 20b + -3b + 3c + 4c = 0 Combine like terms: 12a + -3a = 9a 9a + 20b + -3b + 3c + 4c = 0 Combine like terms: 20b + -3b = 17b 9a + 17b + 3c + 4c = 0 Combine like terms: 3c + 4c = 7c 9a + 17b + 7c = 0 Solving 9a + 17b + 7c = 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. 9a + 17b + -17b + 7c = 0 + -17b Combine like terms: 17b + -17b = 0 9a + 0 + 7c = 0 + -17b 9a + 7c = 0 + -17b Remove the zero: 9a + 7c = -17b Add '-7c' to each side of the equation. 9a + 7c + -7c = -17b + -7c Combine like terms: 7c + -7c = 0 9a + 0 = -17b + -7c 9a = -17b + -7c Divide each side by '9'. a = -1.888888889b + -0.7777777778c Simplifying a = -1.888888889b + -0.7777777778c
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