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Simplifying (2a + 3b + c) + (a + 3b + 4c) = 0 Remove parenthesis around (2a + 3b + c) 2a + 3b + c + (a + 3b + 4c) = 0 Remove parenthesis around (a + 3b + 4c) 2a + 3b + c + a + 3b + 4c = 0 Reorder the terms: 2a + a + 3b + 3b + c + 4c = 0 Combine like terms: 2a + a = 3a 3a + 3b + 3b + c + 4c = 0 Combine like terms: 3b + 3b = 6b 3a + 6b + c + 4c = 0 Combine like terms: c + 4c = 5c 3a + 6b + 5c = 0 Solving 3a + 6b + 5c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 3a + 6b + -6b + 5c = 0 + -6b Combine like terms: 6b + -6b = 0 3a + 0 + 5c = 0 + -6b 3a + 5c = 0 + -6b Remove the zero: 3a + 5c = -6b Add '-5c' to each side of the equation. 3a + 5c + -5c = -6b + -5c Combine like terms: 5c + -5c = 0 3a + 0 = -6b + -5c 3a = -6b + -5c Divide each side by '3'. a = -2b + -1.666666667c Simplifying a = -2b + -1.666666667c
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