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Simplifying 4(a + -3b) + 9(2a + 4b) = 0 (a * 4 + -3b * 4) + 9(2a + 4b) = 0 (4a + -12b) + 9(2a + 4b) = 0 4a + -12b + (2a * 9 + 4b * 9) = 0 4a + -12b + (18a + 36b) = 0 Reorder the terms: 4a + 18a + -12b + 36b = 0 Combine like terms: 4a + 18a = 22a 22a + -12b + 36b = 0 Combine like terms: -12b + 36b = 24b 22a + 24b = 0 Solving 22a + 24b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-24b' to each side of the equation. 22a + 24b + -24b = 0 + -24b Combine like terms: 24b + -24b = 0 22a + 0 = 0 + -24b 22a = 0 + -24b Remove the zero: 22a = -24b Divide each side by '22'. a = -1.090909091b Simplifying a = -1.090909091b
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