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Simplifying ((2a + -4b + 3c) + (3a + 5b + -8)) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Remove parenthesis around (2a + -4b + 3c) (2a + -4b + 3c + (3a + 5b + -8)) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Reorder the terms: (2a + -4b + 3c + (-8 + 3a + 5b)) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Remove parenthesis around (-8 + 3a + 5b) (2a + -4b + 3c + -8 + 3a + 5b) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Reorder the terms: (-8 + 2a + 3a + -4b + 5b + 3c) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Combine like terms: 2a + 3a = 5a (-8 + 5a + -4b + 5b + 3c) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Combine like terms: -4b + 5b = 1b (-8 + 5a + 1b + 3c) + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Remove parenthesis around (-8 + 5a + 1b + 3c) -8 + 5a + 1b + 3c + -1((-1b + -7c) + (6a + 5b + 9c)) = 0 Remove parenthesis around (-1b + -7c) -8 + 5a + 1b + 3c + -1(-1b + -7c + (6a + 5b + 9c)) = 0 Remove parenthesis around (6a + 5b + 9c) -8 + 5a + 1b + 3c + -1(-1b + -7c + 6a + 5b + 9c) = 0 Reorder the terms: -8 + 5a + 1b + 3c + -1(6a + -1b + 5b + -7c + 9c) = 0 Combine like terms: -1b + 5b = 4b -8 + 5a + 1b + 3c + -1(6a + 4b + -7c + 9c) = 0 Combine like terms: -7c + 9c = 2c -8 + 5a + 1b + 3c + -1(6a + 4b + 2c) = 0 -8 + 5a + 1b + 3c + (6a * -1 + 4b * -1 + 2c * -1) = 0 -8 + 5a + 1b + 3c + (-6a + -4b + -2c) = 0 Reorder the terms: -8 + 5a + -6a + 1b + -4b + 3c + -2c = 0 Combine like terms: 5a + -6a = -1a -8 + -1a + 1b + -4b + 3c + -2c = 0 Combine like terms: 1b + -4b = -3b -8 + -1a + -3b + 3c + -2c = 0 Combine like terms: 3c + -2c = 1c -8 + -1a + -3b + 1c = 0 Solving -8 + -1a + -3b + 1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + -1a + -3b + 8 + 1c = 0 + 8 Reorder the terms: -8 + 8 + -1a + -3b + 1c = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1a + -3b + 1c = 0 + 8 -1a + -3b + 1c = 0 + 8 Combine like terms: 0 + 8 = 8 -1a + -3b + 1c = 8 Add '3b' to each side of the equation. -1a + -3b + 3b + 1c = 8 + 3b Combine like terms: -3b + 3b = 0 -1a + 0 + 1c = 8 + 3b -1a + 1c = 8 + 3b Add '-1c' to each side of the equation. -1a + 1c + -1c = 8 + 3b + -1c Combine like terms: 1c + -1c = 0 -1a + 0 = 8 + 3b + -1c -1a = 8 + 3b + -1c Divide each side by '-1'. a = -8 + -3b + c Simplifying a = -8 + -3b + c
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