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Simplifying 5(3a + 5b) + 4(2a + 4b) = 0 (3a * 5 + 5b * 5) + 4(2a + 4b) = 0 (15a + 25b) + 4(2a + 4b) = 0 15a + 25b + (2a * 4 + 4b * 4) = 0 15a + 25b + (8a + 16b) = 0 Reorder the terms: 15a + 8a + 25b + 16b = 0 Combine like terms: 15a + 8a = 23a 23a + 25b + 16b = 0 Combine like terms: 25b + 16b = 41b 23a + 41b = 0 Solving 23a + 41b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-41b' to each side of the equation. 23a + 41b + -41b = 0 + -41b Combine like terms: 41b + -41b = 0 23a + 0 = 0 + -41b 23a = 0 + -41b Remove the zero: 23a = -41b Divide each side by '23'. a = -1.782608696b Simplifying a = -1.782608696b
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