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Simplifying 12a + 11b + 2c + 6c + -5b + -4a = 0 Reorder the terms: 12a + -4a + 11b + -5b + 2c + 6c = 0 Combine like terms: 12a + -4a = 8a 8a + 11b + -5b + 2c + 6c = 0 Combine like terms: 11b + -5b = 6b 8a + 6b + 2c + 6c = 0 Combine like terms: 2c + 6c = 8c 8a + 6b + 8c = 0 Solving 8a + 6b + 8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 8a + 6b + -6b + 8c = 0 + -6b Combine like terms: 6b + -6b = 0 8a + 0 + 8c = 0 + -6b 8a + 8c = 0 + -6b Remove the zero: 8a + 8c = -6b Add '-8c' to each side of the equation. 8a + 8c + -8c = -6b + -8c Combine like terms: 8c + -8c = 0 8a + 0 = -6b + -8c 8a = -6b + -8c Divide each side by '8'. a = -0.75b + -1c Simplifying a = -0.75b + -1c
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