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Simplifying 5(3a + -2b) + -2(3a + 5b) = 0 (3a * 5 + -2b * 5) + -2(3a + 5b) = 0 (15a + -10b) + -2(3a + 5b) = 0 15a + -10b + (3a * -2 + 5b * -2) = 0 15a + -10b + (-6a + -10b) = 0 Reorder the terms: 15a + -6a + -10b + -10b = 0 Combine like terms: 15a + -6a = 9a 9a + -10b + -10b = 0 Combine like terms: -10b + -10b = -20b 9a + -20b = 0 Solving 9a + -20b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20b' to each side of the equation. 9a + -20b + 20b = 0 + 20b Combine like terms: -20b + 20b = 0 9a + 0 = 0 + 20b 9a = 0 + 20b Remove the zero: 9a = 20b Divide each side by '9'. a = 2.222222222b Simplifying a = 2.222222222b
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