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Simplifying 4(b + 9c) + 3(12a + 9b) + -1a + 4(b + c) = 0 (b * 4 + 9c * 4) + 3(12a + 9b) + -1a + 4(b + c) = 0 (4b + 36c) + 3(12a + 9b) + -1a + 4(b + c) = 0 4b + 36c + (12a * 3 + 9b * 3) + -1a + 4(b + c) = 0 4b + 36c + (36a + 27b) + -1a + 4(b + c) = 0 4b + 36c + 36a + 27b + -1a + (b * 4 + c * 4) = 0 4b + 36c + 36a + 27b + -1a + (4b + 4c) = 0 Reorder the terms: 36a + -1a + 4b + 27b + 4b + 36c + 4c = 0 Combine like terms: 36a + -1a = 35a 35a + 4b + 27b + 4b + 36c + 4c = 0 Combine like terms: 4b + 27b = 31b 35a + 31b + 4b + 36c + 4c = 0 Combine like terms: 31b + 4b = 35b 35a + 35b + 36c + 4c = 0 Combine like terms: 36c + 4c = 40c 35a + 35b + 40c = 0 Solving 35a + 35b + 40c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-35b' to each side of the equation. 35a + 35b + -35b + 40c = 0 + -35b Combine like terms: 35b + -35b = 0 35a + 0 + 40c = 0 + -35b 35a + 40c = 0 + -35b Remove the zero: 35a + 40c = -35b Add '-40c' to each side of the equation. 35a + 40c + -40c = -35b + -40c Combine like terms: 40c + -40c = 0 35a + 0 = -35b + -40c 35a = -35b + -40c Divide each side by '35'. a = -1b + -1.142857143c Simplifying a = -1b + -1.142857143c
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