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Simplifying 12a + 18b + 2c + 2c + -3b + -4a = 0 Reorder the terms: 12a + -4a + 18b + -3b + 2c + 2c = 0 Combine like terms: 12a + -4a = 8a 8a + 18b + -3b + 2c + 2c = 0 Combine like terms: 18b + -3b = 15b 8a + 15b + 2c + 2c = 0 Combine like terms: 2c + 2c = 4c 8a + 15b + 4c = 0 Solving 8a + 15b + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15b' to each side of the equation. 8a + 15b + -15b + 4c = 0 + -15b Combine like terms: 15b + -15b = 0 8a + 0 + 4c = 0 + -15b 8a + 4c = 0 + -15b Remove the zero: 8a + 4c = -15b Add '-4c' to each side of the equation. 8a + 4c + -4c = -15b + -4c Combine like terms: 4c + -4c = 0 8a + 0 = -15b + -4c 8a = -15b + -4c Divide each side by '8'. a = -1.875b + -0.5c Simplifying a = -1.875b + -0.5c
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