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Simplifying 4(2a + 4b) + 5(2a + 3b) = 0 (2a * 4 + 4b * 4) + 5(2a + 3b) = 0 (8a + 16b) + 5(2a + 3b) = 0 8a + 16b + (2a * 5 + 3b * 5) = 0 8a + 16b + (10a + 15b) = 0 Reorder the terms: 8a + 10a + 16b + 15b = 0 Combine like terms: 8a + 10a = 18a 18a + 16b + 15b = 0 Combine like terms: 16b + 15b = 31b 18a + 31b = 0 Solving 18a + 31b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-31b' to each side of the equation. 18a + 31b + -31b = 0 + -31b Combine like terms: 31b + -31b = 0 18a + 0 = 0 + -31b 18a = 0 + -31b Remove the zero: 18a = -31b Divide each side by '18'. a = -1.722222222b Simplifying a = -1.722222222b
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