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Simplifying 6(2a + -1b) + -3(3b + -5a) = 0 (2a * 6 + -1b * 6) + -3(3b + -5a) = 0 (12a + -6b) + -3(3b + -5a) = 0 Reorder the terms: 12a + -6b + -3(-5a + 3b) = 0 12a + -6b + (-5a * -3 + 3b * -3) = 0 12a + -6b + (15a + -9b) = 0 Reorder the terms: 12a + 15a + -6b + -9b = 0 Combine like terms: 12a + 15a = 27a 27a + -6b + -9b = 0 Combine like terms: -6b + -9b = -15b 27a + -15b = 0 Solving 27a + -15b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15b' to each side of the equation. 27a + -15b + 15b = 0 + 15b Combine like terms: -15b + 15b = 0 27a + 0 = 0 + 15b 27a = 0 + 15b Remove the zero: 27a = 15b Divide each side by '27'. a = 0.5555555556b Simplifying a = 0.5555555556b
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