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Simplifying 5(a + 2b) + 3(3a + b) = 0 (a * 5 + 2b * 5) + 3(3a + b) = 0 (5a + 10b) + 3(3a + b) = 0 5a + 10b + (3a * 3 + b * 3) = 0 5a + 10b + (9a + 3b) = 0 Reorder the terms: 5a + 9a + 10b + 3b = 0 Combine like terms: 5a + 9a = 14a 14a + 10b + 3b = 0 Combine like terms: 10b + 3b = 13b 14a + 13b = 0 Solving 14a + 13b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 14a + 13b + -13b = 0 + -13b Combine like terms: 13b + -13b = 0 14a + 0 = 0 + -13b 14a = 0 + -13b Remove the zero: 14a = -13b Divide each side by '14'. a = -0.9285714286b Simplifying a = -0.9285714286b
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