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Simplifying 2(a + 2b) + 3(2a + -1b) = 0 (a * 2 + 2b * 2) + 3(2a + -1b) = 0 (2a + 4b) + 3(2a + -1b) = 0 2a + 4b + (2a * 3 + -1b * 3) = 0 2a + 4b + (6a + -3b) = 0 Reorder the terms: 2a + 6a + 4b + -3b = 0 Combine like terms: 2a + 6a = 8a 8a + 4b + -3b = 0 Combine like terms: 4b + -3b = 1b 8a + 1b = 0 Solving 8a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 8a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 8a + 0 = 0 + -1b 8a = 0 + -1b Remove the zero: 8a = -1b Divide each side by '8'. a = -0.125b Simplifying a = -0.125b
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