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