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Simplifying 5(2a + 3b) + 2(3a + 4b) = 0 (2a * 5 + 3b * 5) + 2(3a + 4b) = 0 (10a + 15b) + 2(3a + 4b) = 0 10a + 15b + (3a * 2 + 4b * 2) = 0 10a + 15b + (6a + 8b) = 0 Reorder the terms: 10a + 6a + 15b + 8b = 0 Combine like terms: 10a + 6a = 16a 16a + 15b + 8b = 0 Combine like terms: 15b + 8b = 23b 16a + 23b = 0 Solving 16a + 23b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-23b' to each side of the equation. 16a + 23b + -23b = 0 + -23b Combine like terms: 23b + -23b = 0 16a + 0 = 0 + -23b 16a = 0 + -23b Remove the zero: 16a = -23b Divide each side by '16'. a = -1.4375b Simplifying a = -1.4375b
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