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Simplifying (3a + 5b + -4c) + (2a + -3b + 7c) + (-1a + 4b + -2c) = 0 Remove parenthesis around (3a + 5b + -4c) 3a + 5b + -4c + (2a + -3b + 7c) + (-1a + 4b + -2c) = 0 Remove parenthesis around (2a + -3b + 7c) 3a + 5b + -4c + 2a + -3b + 7c + (-1a + 4b + -2c) = 0 Remove parenthesis around (-1a + 4b + -2c) 3a + 5b + -4c + 2a + -3b + 7c + -1a + 4b + -2c = 0 Reorder the terms: 3a + 2a + -1a + 5b + -3b + 4b + -4c + 7c + -2c = 0 Combine like terms: 3a + 2a = 5a 5a + -1a + 5b + -3b + 4b + -4c + 7c + -2c = 0 Combine like terms: 5a + -1a = 4a 4a + 5b + -3b + 4b + -4c + 7c + -2c = 0 Combine like terms: 5b + -3b = 2b 4a + 2b + 4b + -4c + 7c + -2c = 0 Combine like terms: 2b + 4b = 6b 4a + 6b + -4c + 7c + -2c = 0 Combine like terms: -4c + 7c = 3c 4a + 6b + 3c + -2c = 0 Combine like terms: 3c + -2c = 1c 4a + 6b + 1c = 0 Solving 4a + 6b + 1c = 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. 4a + 6b + -6b + 1c = 0 + -6b Combine like terms: 6b + -6b = 0 4a + 0 + 1c = 0 + -6b 4a + 1c = 0 + -6b Remove the zero: 4a + 1c = -6b Add '-1c' to each side of the equation. 4a + 1c + -1c = -6b + -1c Combine like terms: 1c + -1c = 0 4a + 0 = -6b + -1c 4a = -6b + -1c Divide each side by '4'. a = -1.5b + -0.25c Simplifying a = -1.5b + -0.25c
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