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Simplifying -5b + -1a + -1(3b + -2c) + c + -1(a + -2b + -1c) = 0 -5b + -1a + (3b * -1 + -2c * -1) + c + -1(a + -2b + -1c) = 0 -5b + -1a + (-3b + 2c) + c + -1(a + -2b + -1c) = 0 -5b + -1a + -3b + 2c + c + (a * -1 + -2b * -1 + -1c * -1) = 0 -5b + -1a + -3b + 2c + c + (-1a + 2b + 1c) = 0 Reorder the terms: -1a + -1a + -5b + -3b + 2b + 2c + c + 1c = 0 Combine like terms: -1a + -1a = -2a -2a + -5b + -3b + 2b + 2c + c + 1c = 0 Combine like terms: -5b + -3b = -8b -2a + -8b + 2b + 2c + c + 1c = 0 Combine like terms: -8b + 2b = -6b -2a + -6b + 2c + c + 1c = 0 Combine like terms: 2c + c = 3c -2a + -6b + 3c + 1c = 0 Combine like terms: 3c + 1c = 4c -2a + -6b + 4c = 0 Solving -2a + -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. -2a + -6b + 6b + 4c = 0 + 6b Combine like terms: -6b + 6b = 0 -2a + 0 + 4c = 0 + 6b -2a + 4c = 0 + 6b Remove the zero: -2a + 4c = 6b Add '-4c' to each side of the equation. -2a + 4c + -4c = 6b + -4c Combine like terms: 4c + -4c = 0 -2a + 0 = 6b + -4c -2a = 6b + -4c Divide each side by '-2'. a = -3b + 2c Simplifying a = -3b + 2c
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