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Simplifying 12(3a + -2b) + 4(3a + 3b) = 0 (3a * 12 + -2b * 12) + 4(3a + 3b) = 0 (36a + -24b) + 4(3a + 3b) = 0 36a + -24b + (3a * 4 + 3b * 4) = 0 36a + -24b + (12a + 12b) = 0 Reorder the terms: 36a + 12a + -24b + 12b = 0 Combine like terms: 36a + 12a = 48a 48a + -24b + 12b = 0 Combine like terms: -24b + 12b = -12b 48a + -12b = 0 Solving 48a + -12b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12b' to each side of the equation. 48a + -12b + 12b = 0 + 12b Combine like terms: -12b + 12b = 0 48a + 0 = 0 + 12b 48a = 0 + 12b Remove the zero: 48a = 12b Divide each side by '48'. a = 0.25b Simplifying a = 0.25b
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