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Simplifying 3(6a + b) + 6(5a + 4b) = 0 (6a * 3 + b * 3) + 6(5a + 4b) = 0 (18a + 3b) + 6(5a + 4b) = 0 18a + 3b + (5a * 6 + 4b * 6) = 0 18a + 3b + (30a + 24b) = 0 Reorder the terms: 18a + 30a + 3b + 24b = 0 Combine like terms: 18a + 30a = 48a 48a + 3b + 24b = 0 Combine like terms: 3b + 24b = 27b 48a + 27b = 0 Solving 48a + 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. 48a + 27b + -27b = 0 + -27b Combine like terms: 27b + -27b = 0 48a + 0 = 0 + -27b 48a = 0 + -27b Remove the zero: 48a = -27b Divide each side by '48'. a = -0.5625b Simplifying a = -0.5625b
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