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Simplifying a + 6b + -2c + 4a + -4b + 5c = 0 Reorder the terms: a + 4a + 6b + -4b + -2c + 5c = 0 Combine like terms: a + 4a = 5a 5a + 6b + -4b + -2c + 5c = 0 Combine like terms: 6b + -4b = 2b 5a + 2b + -2c + 5c = 0 Combine like terms: -2c + 5c = 3c 5a + 2b + 3c = 0 Solving 5a + 2b + 3c = 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. 5a + 2b + -2b + 3c = 0 + -2b Combine like terms: 2b + -2b = 0 5a + 0 + 3c = 0 + -2b 5a + 3c = 0 + -2b Remove the zero: 5a + 3c = -2b Add '-3c' to each side of the equation. 5a + 3c + -3c = -2b + -3c Combine like terms: 3c + -3c = 0 5a + 0 = -2b + -3c 5a = -2b + -3c Divide each side by '5'. a = -0.4b + -0.6c Simplifying a = -0.4b + -0.6c
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