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Simplifying (3a + 4b + c) + (5a + -4b + 2c) = 0 Remove parenthesis around (3a + 4b + c) 3a + 4b + c + (5a + -4b + 2c) = 0 Remove parenthesis around (5a + -4b + 2c) 3a + 4b + c + 5a + -4b + 2c = 0 Reorder the terms: 3a + 5a + 4b + -4b + c + 2c = 0 Combine like terms: 3a + 5a = 8a 8a + 4b + -4b + c + 2c = 0 Combine like terms: 4b + -4b = 0 8a + 0 + c + 2c = 0 8a + c + 2c = 0 Combine like terms: c + 2c = 3c 8a + 3c = 0 Solving 8a + 3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3c' to each side of the equation. 8a + 3c + -3c = 0 + -3c Combine like terms: 3c + -3c = 0 8a + 0 = 0 + -3c 8a = 0 + -3c Remove the zero: 8a = -3c Divide each side by '8'. a = -0.375c Simplifying a = -0.375c
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