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Simplifying a + -1[5b + -1[a + -1(3b + -2c) + c + -1(a + -2b + -1c)]] = 0 a + -1[5b + -1[a + (3b * -1 + -2c * -1) + c + -1(a + -2b + -1c)]] = 0 a + -1[5b + -1[a + (-3b + 2c) + c + -1(a + -2b + -1c)]] = 0 a + -1[5b + -1[a + -3b + 2c + c + (a * -1 + -2b * -1 + -1c * -1)]] = 0 a + -1[5b + -1[a + -3b + 2c + c + (-1a + 2b + 1c)]] = 0 Reorder the terms: a + -1[5b + -1[a + -1a + -3b + 2b + 2c + c + 1c]] = 0 Combine like terms: a + -1a = 0 a + -1[5b + -1[0 + -3b + 2b + 2c + c + 1c]] = 0 a + -1[5b + -1[-3b + 2b + 2c + c + 1c]] = 0 Combine like terms: -3b + 2b = -1b a + -1[5b + -1[-1b + 2c + c + 1c]] = 0 Combine like terms: 2c + c = 3c a + -1[5b + -1[-1b + 3c + 1c]] = 0 Combine like terms: 3c + 1c = 4c a + -1[5b + -1[-1b + 4c]] = 0 a + -1[5b + [-1b * -1 + 4c * -1]] = 0 a + -1[5b + [1b + -4c]] = 0 Combine like terms: 5b + 1b = 6b a + -1[6b + -4c] = 0 a + [6b * -1 + -4c * -1] = 0 a + [-6b + 4c] = 0 Solving a + -6b + 4c = 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. a + -6b + 6b + 4c = 0 + 6b Combine like terms: -6b + 6b = 0 a + 0 + 4c = 0 + 6b a + 4c = 0 + 6b Remove the zero: a + 4c = 6b Add '-4c' to each side of the equation. a + 4c + -4c = 6b + -4c Combine like terms: 4c + -4c = 0 a + 0 = 6b + -4c a = 6b + -4c Simplifying a = 6b + -4c
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