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Simplifying (6a + 8b + -4c) + (4b + -14c) + -1(2a + -1b + 7c) = 0 Remove parenthesis around (6a + 8b + -4c) 6a + 8b + -4c + (4b + -14c) + -1(2a + -1b + 7c) = 0 Remove parenthesis around (4b + -14c) 6a + 8b + -4c + 4b + -14c + -1(2a + -1b + 7c) = 0 6a + 8b + -4c + 4b + -14c + (2a * -1 + -1b * -1 + 7c * -1) = 0 6a + 8b + -4c + 4b + -14c + (-2a + 1b + -7c) = 0 Reorder the terms: 6a + -2a + 8b + 4b + 1b + -4c + -14c + -7c = 0 Combine like terms: 6a + -2a = 4a 4a + 8b + 4b + 1b + -4c + -14c + -7c = 0 Combine like terms: 8b + 4b = 12b 4a + 12b + 1b + -4c + -14c + -7c = 0 Combine like terms: 12b + 1b = 13b 4a + 13b + -4c + -14c + -7c = 0 Combine like terms: -4c + -14c = -18c 4a + 13b + -18c + -7c = 0 Combine like terms: -18c + -7c = -25c 4a + 13b + -25c = 0 Solving 4a + 13b + -25c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 4a + 13b + -13b + -25c = 0 + -13b Combine like terms: 13b + -13b = 0 4a + 0 + -25c = 0 + -13b 4a + -25c = 0 + -13b Remove the zero: 4a + -25c = -13b Add '25c' to each side of the equation. 4a + -25c + 25c = -13b + 25c Combine like terms: -25c + 25c = 0 4a + 0 = -13b + 25c 4a = -13b + 25c Divide each side by '4'. a = -3.25b + 6.25c Simplifying a = -3.25b + 6.25c
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