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Simplifying 4(2a + b) + 3(4a + 2b) = 0 (2a * 4 + b * 4) + 3(4a + 2b) = 0 (8a + 4b) + 3(4a + 2b) = 0 8a + 4b + (4a * 3 + 2b * 3) = 0 8a + 4b + (12a + 6b) = 0 Reorder the terms: 8a + 12a + 4b + 6b = 0 Combine like terms: 8a + 12a = 20a 20a + 4b + 6b = 0 Combine like terms: 4b + 6b = 10b 20a + 10b = 0 Solving 20a + 10b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10b' to each side of the equation. 20a + 10b + -10b = 0 + -10b Combine like terms: 10b + -10b = 0 20a + 0 = 0 + -10b 20a = 0 + -10b Remove the zero: 20a = -10b Divide each side by '20'. a = -0.5b Simplifying a = -0.5b
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