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Simplifying 5(6a + 5b) + 3(5a + 3b) = 0 (6a * 5 + 5b * 5) + 3(5a + 3b) = 0 (30a + 25b) + 3(5a + 3b) = 0 30a + 25b + (5a * 3 + 3b * 3) = 0 30a + 25b + (15a + 9b) = 0 Reorder the terms: 30a + 15a + 25b + 9b = 0 Combine like terms: 30a + 15a = 45a 45a + 25b + 9b = 0 Combine like terms: 25b + 9b = 34b 45a + 34b = 0 Solving 45a + 34b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-34b' to each side of the equation. 45a + 34b + -34b = 0 + -34b Combine like terms: 34b + -34b = 0 45a + 0 = 0 + -34b 45a = 0 + -34b Remove the zero: 45a = -34b Divide each side by '45'. a = -0.7555555556b Simplifying a = -0.7555555556b
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