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Simplifying 6(3a + -1b) + -3(3b + -2a) = 0 (3a * 6 + -1b * 6) + -3(3b + -2a) = 0 (18a + -6b) + -3(3b + -2a) = 0 Reorder the terms: 18a + -6b + -3(-2a + 3b) = 0 18a + -6b + (-2a * -3 + 3b * -3) = 0 18a + -6b + (6a + -9b) = 0 Reorder the terms: 18a + 6a + -6b + -9b = 0 Combine like terms: 18a + 6a = 24a 24a + -6b + -9b = 0 Combine like terms: -6b + -9b = -15b 24a + -15b = 0 Solving 24a + -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. 24a + -15b + 15b = 0 + 15b Combine like terms: -15b + 15b = 0 24a + 0 = 0 + 15b 24a = 0 + 15b Remove the zero: 24a = 15b Divide each side by '24'. a = 0.625b Simplifying a = 0.625b
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