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Simplifying 3(4a + -2c) + -2(2a + 4c) = 0 (4a * 3 + -2c * 3) + -2(2a + 4c) = 0 (12a + -6c) + -2(2a + 4c) = 0 12a + -6c + (2a * -2 + 4c * -2) = 0 12a + -6c + (-4a + -8c) = 0 Reorder the terms: 12a + -4a + -6c + -8c = 0 Combine like terms: 12a + -4a = 8a 8a + -6c + -8c = 0 Combine like terms: -6c + -8c = -14c 8a + -14c = 0 Solving 8a + -14c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14c' to each side of the equation. 8a + -14c + 14c = 0 + 14c Combine like terms: -14c + 14c = 0 8a + 0 = 0 + 14c 8a = 0 + 14c Remove the zero: 8a = 14c Divide each side by '8'. a = 1.75c Simplifying a = 1.75c
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