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Simplifying 5a + 2b + c + 3a + 5b + 2c = 0 Reorder the terms: 5a + 3a + 2b + 5b + c + 2c = 0 Combine like terms: 5a + 3a = 8a 8a + 2b + 5b + c + 2c = 0 Combine like terms: 2b + 5b = 7b 8a + 7b + c + 2c = 0 Combine like terms: c + 2c = 3c 8a + 7b + 3c = 0 Solving 8a + 7b + 3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7b' to each side of the equation. 8a + 7b + -7b + 3c = 0 + -7b Combine like terms: 7b + -7b = 0 8a + 0 + 3c = 0 + -7b 8a + 3c = 0 + -7b Remove the zero: 8a + 3c = -7b Add '-3c' to each side of the equation. 8a + 3c + -3c = -7b + -3c Combine like terms: 3c + -3c = 0 8a + 0 = -7b + -3c 8a = -7b + -3c Divide each side by '8'. a = -0.875b + -0.375c Simplifying a = -0.875b + -0.375c
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