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Simplifying 3(5a + -1b) + -5(3b + -6a) = 0 (5a * 3 + -1b * 3) + -5(3b + -6a) = 0 (15a + -3b) + -5(3b + -6a) = 0 Reorder the terms: 15a + -3b + -5(-6a + 3b) = 0 15a + -3b + (-6a * -5 + 3b * -5) = 0 15a + -3b + (30a + -15b) = 0 Reorder the terms: 15a + 30a + -3b + -15b = 0 Combine like terms: 15a + 30a = 45a 45a + -3b + -15b = 0 Combine like terms: -3b + -15b = -18b 45a + -18b = 0 Solving 45a + -18b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18b' to each side of the equation. 45a + -18b + 18b = 0 + 18b Combine like terms: -18b + 18b = 0 45a + 0 = 0 + 18b 45a = 0 + 18b Remove the zero: 45a = 18b Divide each side by '45'. a = 0.4b Simplifying a = 0.4b
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