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Simplifying 2(4a + -2c) + -1(3a + -2c) + (7a + -1c) = 0 (4a * 2 + -2c * 2) + -1(3a + -2c) + (7a + -1c) = 0 (8a + -4c) + -1(3a + -2c) + (7a + -1c) = 0 8a + -4c + (3a * -1 + -2c * -1) + (7a + -1c) = 0 8a + -4c + (-3a + 2c) + (7a + -1c) = 0 Remove parenthesis around (7a + -1c) 8a + -4c + -3a + 2c + 7a + -1c = 0 Reorder the terms: 8a + -3a + 7a + -4c + 2c + -1c = 0 Combine like terms: 8a + -3a = 5a 5a + 7a + -4c + 2c + -1c = 0 Combine like terms: 5a + 7a = 12a 12a + -4c + 2c + -1c = 0 Combine like terms: -4c + 2c = -2c 12a + -2c + -1c = 0 Combine like terms: -2c + -1c = -3c 12a + -3c = 0 Solving 12a + -3c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3c' to each side of the equation. 12a + -3c + 3c = 0 + 3c Combine like terms: -3c + 3c = 0 12a + 0 = 0 + 3c 12a = 0 + 3c Remove the zero: 12a = 3c Divide each side by '12'. a = 0.25c Simplifying a = 0.25c
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