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Simplifying 4(2a + b) + 5(2a + 5b) = 0 (2a * 4 + b * 4) + 5(2a + 5b) = 0 (8a + 4b) + 5(2a + 5b) = 0 8a + 4b + (2a * 5 + 5b * 5) = 0 8a + 4b + (10a + 25b) = 0 Reorder the terms: 8a + 10a + 4b + 25b = 0 Combine like terms: 8a + 10a = 18a 18a + 4b + 25b = 0 Combine like terms: 4b + 25b = 29b 18a + 29b = 0 Solving 18a + 29b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-29b' to each side of the equation. 18a + 29b + -29b = 0 + -29b Combine like terms: 29b + -29b = 0 18a + 0 = 0 + -29b 18a = 0 + -29b Remove the zero: 18a = -29b Divide each side by '18'. a = -1.611111111b Simplifying a = -1.611111111b
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