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Simplifying 5(3a + -1b) + -6(8b + -6a) = 0 (3a * 5 + -1b * 5) + -6(8b + -6a) = 0 (15a + -5b) + -6(8b + -6a) = 0 Reorder the terms: 15a + -5b + -6(-6a + 8b) = 0 15a + -5b + (-6a * -6 + 8b * -6) = 0 15a + -5b + (36a + -48b) = 0 Reorder the terms: 15a + 36a + -5b + -48b = 0 Combine like terms: 15a + 36a = 51a 51a + -5b + -48b = 0 Combine like terms: -5b + -48b = -53b 51a + -53b = 0 Solving 51a + -53b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '53b' to each side of the equation. 51a + -53b + 53b = 0 + 53b Combine like terms: -53b + 53b = 0 51a + 0 = 0 + 53b 51a = 0 + 53b Remove the zero: 51a = 53b Divide each side by '51'. a = 1.039215686b Simplifying a = 1.039215686b
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