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Simplifying 5(3b + -2a) + 6(2a + -1b) = 0 Reorder the terms: 5(-2a + 3b) + 6(2a + -1b) = 0 (-2a * 5 + 3b * 5) + 6(2a + -1b) = 0 (-10a + 15b) + 6(2a + -1b) = 0 -10a + 15b + (2a * 6 + -1b * 6) = 0 -10a + 15b + (12a + -6b) = 0 Reorder the terms: -10a + 12a + 15b + -6b = 0 Combine like terms: -10a + 12a = 2a 2a + 15b + -6b = 0 Combine like terms: 15b + -6b = 9b 2a + 9b = 0 Solving 2a + 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. 2a + 9b + -9b = 0 + -9b Combine like terms: 9b + -9b = 0 2a + 0 = 0 + -9b 2a = 0 + -9b Remove the zero: 2a = -9b Divide each side by '2'. a = -4.5b Simplifying a = -4.5b
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