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Simplifying 3a + 4b + 5c + 6a + -3b + -7c + -3a + 2b + 3c = 0 Reorder the terms: 3a + 6a + -3a + 4b + -3b + 2b + 5c + -7c + 3c = 0 Combine like terms: 3a + 6a = 9a 9a + -3a + 4b + -3b + 2b + 5c + -7c + 3c = 0 Combine like terms: 9a + -3a = 6a 6a + 4b + -3b + 2b + 5c + -7c + 3c = 0 Combine like terms: 4b + -3b = 1b 6a + 1b + 2b + 5c + -7c + 3c = 0 Combine like terms: 1b + 2b = 3b 6a + 3b + 5c + -7c + 3c = 0 Combine like terms: 5c + -7c = -2c 6a + 3b + -2c + 3c = 0 Combine like terms: -2c + 3c = 1c 6a + 3b + 1c = 0 Solving 6a + 3b + 1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 6a + 3b + -3b + 1c = 0 + -3b Combine like terms: 3b + -3b = 0 6a + 0 + 1c = 0 + -3b 6a + 1c = 0 + -3b Remove the zero: 6a + 1c = -3b Add '-1c' to each side of the equation. 6a + 1c + -1c = -3b + -1c Combine like terms: 1c + -1c = 0 6a + 0 = -3b + -1c 6a = -3b + -1c Divide each side by '6'. a = -0.5b + -0.1666666667c Simplifying a = -0.5b + -0.1666666667c
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