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Simplifying 2(4a + -1b) + 3(b + 5a) = 0 (4a * 2 + -1b * 2) + 3(b + 5a) = 0 (8a + -2b) + 3(b + 5a) = 0 Reorder the terms: 8a + -2b + 3(5a + b) = 0 8a + -2b + (5a * 3 + b * 3) = 0 8a + -2b + (15a + 3b) = 0 Reorder the terms: 8a + 15a + -2b + 3b = 0 Combine like terms: 8a + 15a = 23a 23a + -2b + 3b = 0 Combine like terms: -2b + 3b = 1b 23a + 1b = 0 Solving 23a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 23a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 23a + 0 = 0 + -1b 23a = 0 + -1b Remove the zero: 23a = -1b Divide each side by '23'. a = -0.04347826087b Simplifying a = -0.04347826087b
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