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Simplifying 5(3a + 2b) + 5(3a + 3b) = 0 (3a * 5 + 2b * 5) + 5(3a + 3b) = 0 (15a + 10b) + 5(3a + 3b) = 0 15a + 10b + (3a * 5 + 3b * 5) = 0 15a + 10b + (15a + 15b) = 0 Reorder the terms: 15a + 15a + 10b + 15b = 0 Combine like terms: 15a + 15a = 30a 30a + 10b + 15b = 0 Combine like terms: 10b + 15b = 25b 30a + 25b = 0 Solving 30a + 25b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-25b' to each side of the equation. 30a + 25b + -25b = 0 + -25b Combine like terms: 25b + -25b = 0 30a + 0 = 0 + -25b 30a = 0 + -25b Remove the zero: 30a = -25b Divide each side by '30'. a = -0.8333333333b Simplifying a = -0.8333333333b
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