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Simplifying 3(4a + 5b) + 5(a + 2b) = 0 (4a * 3 + 5b * 3) + 5(a + 2b) = 0 (12a + 15b) + 5(a + 2b) = 0 12a + 15b + (a * 5 + 2b * 5) = 0 12a + 15b + (5a + 10b) = 0 Reorder the terms: 12a + 5a + 15b + 10b = 0 Combine like terms: 12a + 5a = 17a 17a + 15b + 10b = 0 Combine like terms: 15b + 10b = 25b 17a + 25b = 0 Solving 17a + 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. 17a + 25b + -25b = 0 + -25b Combine like terms: 25b + -25b = 0 17a + 0 = 0 + -25b 17a = 0 + -25b Remove the zero: 17a = -25b Divide each side by '17'. a = -1.470588235b Simplifying a = -1.470588235b
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