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Simplifying 3(4a + -1b) + -6(8b + -8a) = 0 (4a * 3 + -1b * 3) + -6(8b + -8a) = 0 (12a + -3b) + -6(8b + -8a) = 0 Reorder the terms: 12a + -3b + -6(-8a + 8b) = 0 12a + -3b + (-8a * -6 + 8b * -6) = 0 12a + -3b + (48a + -48b) = 0 Reorder the terms: 12a + 48a + -3b + -48b = 0 Combine like terms: 12a + 48a = 60a 60a + -3b + -48b = 0 Combine like terms: -3b + -48b = -51b 60a + -51b = 0 Solving 60a + -51b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '51b' to each side of the equation. 60a + -51b + 51b = 0 + 51b Combine like terms: -51b + 51b = 0 60a + 0 = 0 + 51b 60a = 0 + 51b Remove the zero: 60a = 51b Divide each side by '60'. a = 0.85b Simplifying a = 0.85b
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