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Simplifying 3(6a + 2b) + 7(5a + 4b) = 0 (6a * 3 + 2b * 3) + 7(5a + 4b) = 0 (18a + 6b) + 7(5a + 4b) = 0 18a + 6b + (5a * 7 + 4b * 7) = 0 18a + 6b + (35a + 28b) = 0 Reorder the terms: 18a + 35a + 6b + 28b = 0 Combine like terms: 18a + 35a = 53a 53a + 6b + 28b = 0 Combine like terms: 6b + 28b = 34b 53a + 34b = 0 Solving 53a + 34b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-34b' to each side of the equation. 53a + 34b + -34b = 0 + -34b Combine like terms: 34b + -34b = 0 53a + 0 = 0 + -34b 53a = 0 + -34b Remove the zero: 53a = -34b Divide each side by '53'. a = -0.641509434b Simplifying a = -0.641509434b
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