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Simplifying 2(a + 3b) + 4(2a + -1b) = 0 (a * 2 + 3b * 2) + 4(2a + -1b) = 0 (2a + 6b) + 4(2a + -1b) = 0 2a + 6b + (2a * 4 + -1b * 4) = 0 2a + 6b + (8a + -4b) = 0 Reorder the terms: 2a + 8a + 6b + -4b = 0 Combine like terms: 2a + 8a = 10a 10a + 6b + -4b = 0 Combine like terms: 6b + -4b = 2b 10a + 2b = 0 Solving 10a + 2b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 10a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 10a + 0 = 0 + -2b 10a = 0 + -2b Remove the zero: 10a = -2b Divide each side by '10'. a = -0.2b Simplifying a = -0.2b
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