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Simplifying 3(4a + b) + 6(2a + 4b) = 0 (4a * 3 + b * 3) + 6(2a + 4b) = 0 (12a + 3b) + 6(2a + 4b) = 0 12a + 3b + (2a * 6 + 4b * 6) = 0 12a + 3b + (12a + 24b) = 0 Reorder the terms: 12a + 12a + 3b + 24b = 0 Combine like terms: 12a + 12a = 24a 24a + 3b + 24b = 0 Combine like terms: 3b + 24b = 27b 24a + 27b = 0 Solving 24a + 27b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-27b' to each side of the equation. 24a + 27b + -27b = 0 + -27b Combine like terms: 27b + -27b = 0 24a + 0 = 0 + -27b 24a = 0 + -27b Remove the zero: 24a = -27b Divide each side by '24'. a = -1.125b Simplifying a = -1.125b
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