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Simplifying 19a + 14b + 4c + 6c + -6b + -3a = 0 Reorder the terms: 19a + -3a + 14b + -6b + 4c + 6c = 0 Combine like terms: 19a + -3a = 16a 16a + 14b + -6b + 4c + 6c = 0 Combine like terms: 14b + -6b = 8b 16a + 8b + 4c + 6c = 0 Combine like terms: 4c + 6c = 10c 16a + 8b + 10c = 0 Solving 16a + 8b + 10c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 16a + 8b + -8b + 10c = 0 + -8b Combine like terms: 8b + -8b = 0 16a + 0 + 10c = 0 + -8b 16a + 10c = 0 + -8b Remove the zero: 16a + 10c = -8b Add '-10c' to each side of the equation. 16a + 10c + -10c = -8b + -10c Combine like terms: 10c + -10c = 0 16a + 0 = -8b + -10c 16a = -8b + -10c Divide each side by '16'. a = -0.5b + -0.625c Simplifying a = -0.5b + -0.625c
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