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Simplifying 6(6a + 5b) + -3(4a + 7b) = 0 (6a * 6 + 5b * 6) + -3(4a + 7b) = 0 (36a + 30b) + -3(4a + 7b) = 0 36a + 30b + (4a * -3 + 7b * -3) = 0 36a + 30b + (-12a + -21b) = 0 Reorder the terms: 36a + -12a + 30b + -21b = 0 Combine like terms: 36a + -12a = 24a 24a + 30b + -21b = 0 Combine like terms: 30b + -21b = 9b 24a + 9b = 0 Solving 24a + 9b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. 24a + 9b + -9b = 0 + -9b Combine like terms: 9b + -9b = 0 24a + 0 = 0 + -9b 24a = 0 + -9b Remove the zero: 24a = -9b Divide each side by '24'. a = -0.375b Simplifying a = -0.375b
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