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