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Simplifying 7(3a + 2b) + 5(4a + 2b) = 0 (3a * 7 + 2b * 7) + 5(4a + 2b) = 0 (21a + 14b) + 5(4a + 2b) = 0 21a + 14b + (4a * 5 + 2b * 5) = 0 21a + 14b + (20a + 10b) = 0 Reorder the terms: 21a + 20a + 14b + 10b = 0 Combine like terms: 21a + 20a = 41a 41a + 14b + 10b = 0 Combine like terms: 14b + 10b = 24b 41a + 24b = 0 Solving 41a + 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. 41a + 24b + -24b = 0 + -24b Combine like terms: 24b + -24b = 0 41a + 0 = 0 + -24b 41a = 0 + -24b Remove the zero: 41a = -24b Divide each side by '41'. a = -0.5853658537b Simplifying a = -0.5853658537b
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