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Simplifying 12a + -8b + 2c + -10a + 4b + -1c = 0 Reorder the terms: 12a + -10a + -8b + 4b + 2c + -1c = 0 Combine like terms: 12a + -10a = 2a 2a + -8b + 4b + 2c + -1c = 0 Combine like terms: -8b + 4b = -4b 2a + -4b + 2c + -1c = 0 Combine like terms: 2c + -1c = 1c 2a + -4b + 1c = 0 Solving 2a + -4b + 1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. 2a + -4b + 4b + 1c = 0 + 4b Combine like terms: -4b + 4b = 0 2a + 0 + 1c = 0 + 4b 2a + 1c = 0 + 4b Remove the zero: 2a + 1c = 4b Add '-1c' to each side of the equation. 2a + 1c + -1c = 4b + -1c Combine like terms: 1c + -1c = 0 2a + 0 = 4b + -1c 2a = 4b + -1c Divide each side by '2'. a = 2b + -0.5c Simplifying a = 2b + -0.5c
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