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Simplifying 3(5a + b) + 4(a + 2b) = 0 (5a * 3 + b * 3) + 4(a + 2b) = 0 (15a + 3b) + 4(a + 2b) = 0 15a + 3b + (a * 4 + 2b * 4) = 0 15a + 3b + (4a + 8b) = 0 Reorder the terms: 15a + 4a + 3b + 8b = 0 Combine like terms: 15a + 4a = 19a 19a + 3b + 8b = 0 Combine like terms: 3b + 8b = 11b 19a + 11b = 0 Solving 19a + 11b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11b' to each side of the equation. 19a + 11b + -11b = 0 + -11b Combine like terms: 11b + -11b = 0 19a + 0 = 0 + -11b 19a = 0 + -11b Remove the zero: 19a = -11b Divide each side by '19'. a = -0.5789473684b Simplifying a = -0.5789473684b
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