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Simplifying a + b + c + 2a + 3b + 4c = 0 Reorder the terms: a + 2a + b + 3b + c + 4c = 0 Combine like terms: a + 2a = 3a 3a + b + 3b + c + 4c = 0 Combine like terms: b + 3b = 4b 3a + 4b + c + 4c = 0 Combine like terms: c + 4c = 5c 3a + 4b + 5c = 0 Solving 3a + 4b + 5c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b + 5c = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 + 5c = 0 + -4b 3a + 5c = 0 + -4b Remove the zero: 3a + 5c = -4b Add '-5c' to each side of the equation. 3a + 5c + -5c = -4b + -5c Combine like terms: 5c + -5c = 0 3a + 0 = -4b + -5c 3a = -4b + -5c Divide each side by '3'. a = -1.333333333b + -1.666666667c Simplifying a = -1.333333333b + -1.666666667c
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