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Simplifying 3a + 2b + -1c + 5a + 3c = 0 Reorder the terms: 3a + 5a + 2b + -1c + 3c = 0 Combine like terms: 3a + 5a = 8a 8a + 2b + -1c + 3c = 0 Combine like terms: -1c + 3c = 2c 8a + 2b + 2c = 0 Solving 8a + 2b + 2c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 8a + 2b + -2b + 2c = 0 + -2b Combine like terms: 2b + -2b = 0 8a + 0 + 2c = 0 + -2b 8a + 2c = 0 + -2b Remove the zero: 8a + 2c = -2b Add '-2c' to each side of the equation. 8a + 2c + -2c = -2b + -2c Combine like terms: 2c + -2c = 0 8a + 0 = -2b + -2c 8a = -2b + -2c Divide each side by '8'. a = -0.25b + -0.25c Simplifying a = -0.25b + -0.25c
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