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Simplifying 3(a + b) + -2(b + -1a) + 4(2a + 3b) = 0 (a * 3 + b * 3) + -2(b + -1a) + 4(2a + 3b) = 0 (3a + 3b) + -2(b + -1a) + 4(2a + 3b) = 0 Reorder the terms: 3a + 3b + -2(-1a + b) + 4(2a + 3b) = 0 3a + 3b + (-1a * -2 + b * -2) + 4(2a + 3b) = 0 3a + 3b + (2a + -2b) + 4(2a + 3b) = 0 3a + 3b + 2a + -2b + (2a * 4 + 3b * 4) = 0 3a + 3b + 2a + -2b + (8a + 12b) = 0 Reorder the terms: 3a + 2a + 8a + 3b + -2b + 12b = 0 Combine like terms: 3a + 2a = 5a 5a + 8a + 3b + -2b + 12b = 0 Combine like terms: 5a + 8a = 13a 13a + 3b + -2b + 12b = 0 Combine like terms: 3b + -2b = 1b 13a + 1b + 12b = 0 Combine like terms: 1b + 12b = 13b 13a + 13b = 0 Solving 13a + 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. 13a + 13b + -13b = 0 + -13b Combine like terms: 13b + -13b = 0 13a + 0 = 0 + -13b 13a = 0 + -13b Remove the zero: 13a = -13b Divide each side by '13'. a = -1b Simplifying a = -1b
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