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Simplifying 5(6a + 3b) + 3(4a + 4b) = 0 (6a * 5 + 3b * 5) + 3(4a + 4b) = 0 (30a + 15b) + 3(4a + 4b) = 0 30a + 15b + (4a * 3 + 4b * 3) = 0 30a + 15b + (12a + 12b) = 0 Reorder the terms: 30a + 12a + 15b + 12b = 0 Combine like terms: 30a + 12a = 42a 42a + 15b + 12b = 0 Combine like terms: 15b + 12b = 27b 42a + 27b = 0 Solving 42a + 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. 42a + 27b + -27b = 0 + -27b Combine like terms: 27b + -27b = 0 42a + 0 = 0 + -27b 42a = 0 + -27b Remove the zero: 42a = -27b Divide each side by '42'. a = -0.6428571429b Simplifying a = -0.6428571429b
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