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Simplifying a + 2b + 3c + 3a + 3a + 3b = 0 Reorder the terms: a + 3a + 3a + 2b + 3b + 3c = 0 Combine like terms: a + 3a = 4a 4a + 3a + 2b + 3b + 3c = 0 Combine like terms: 4a + 3a = 7a 7a + 2b + 3b + 3c = 0 Combine like terms: 2b + 3b = 5b 7a + 5b + 3c = 0 Solving 7a + 5b + 3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 7a + 5b + -5b + 3c = 0 + -5b Combine like terms: 5b + -5b = 0 7a + 0 + 3c = 0 + -5b 7a + 3c = 0 + -5b Remove the zero: 7a + 3c = -5b Add '-3c' to each side of the equation. 7a + 3c + -3c = -5b + -3c Combine like terms: 3c + -3c = 0 7a + 0 = -5b + -3c 7a = -5b + -3c Divide each side by '7'. a = -0.7142857143b + -0.4285714286c Simplifying a = -0.7142857143b + -0.4285714286c
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