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Simplifying 2(3a + 5b) + 3(5a + -3b) = 0 (3a * 2 + 5b * 2) + 3(5a + -3b) = 0 (6a + 10b) + 3(5a + -3b) = 0 6a + 10b + (5a * 3 + -3b * 3) = 0 6a + 10b + (15a + -9b) = 0 Reorder the terms: 6a + 15a + 10b + -9b = 0 Combine like terms: 6a + 15a = 21a 21a + 10b + -9b = 0 Combine like terms: 10b + -9b = 1b 21a + 1b = 0 Solving 21a + 1b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 21a + 1b + -1b = 0 + -1b Combine like terms: 1b + -1b = 0 21a + 0 = 0 + -1b 21a = 0 + -1b Remove the zero: 21a = -1b Divide each side by '21'. a = -0.04761904762b Simplifying a = -0.04761904762b
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