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Simplifying 8(2a + 3b) + 3(b + -5a) = 0 (2a * 8 + 3b * 8) + 3(b + -5a) = 0 (16a + 24b) + 3(b + -5a) = 0 Reorder the terms: 16a + 24b + 3(-5a + b) = 0 16a + 24b + (-5a * 3 + b * 3) = 0 16a + 24b + (-15a + 3b) = 0 Reorder the terms: 16a + -15a + 24b + 3b = 0 Combine like terms: 16a + -15a = 1a 1a + 24b + 3b = 0 Combine like terms: 24b + 3b = 27b 1a + 27b = 0 Solving 1a + 27b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-27b' to each side of the equation. 1a + 27b + -27b = 0 + -27b Combine like terms: 27b + -27b = 0 1a + 0 = 0 + -27b 1a = 0 + -27b Remove the zero: 1a = -27b Divide each side by '1'. a = -27b Simplifying a = -27b
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