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Simplifying 7(3b + c + -4a) + -8(a + -3c + 6b) = 0 Reorder the terms: 7(-4a + 3b + c) + -8(a + -3c + 6b) = 0 (-4a * 7 + 3b * 7 + c * 7) + -8(a + -3c + 6b) = 0 (-28a + 21b + 7c) + -8(a + -3c + 6b) = 0 Reorder the terms: -28a + 21b + 7c + -8(a + 6b + -3c) = 0 -28a + 21b + 7c + (a * -8 + 6b * -8 + -3c * -8) = 0 -28a + 21b + 7c + (-8a + -48b + 24c) = 0 Reorder the terms: -28a + -8a + 21b + -48b + 7c + 24c = 0 Combine like terms: -28a + -8a = -36a -36a + 21b + -48b + 7c + 24c = 0 Combine like terms: 21b + -48b = -27b -36a + -27b + 7c + 24c = 0 Combine like terms: 7c + 24c = 31c -36a + -27b + 31c = 0 Solving -36a + -27b + 31c = 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. -36a + -27b + 27b + 31c = 0 + 27b Combine like terms: -27b + 27b = 0 -36a + 0 + 31c = 0 + 27b -36a + 31c = 0 + 27b Remove the zero: -36a + 31c = 27b Add '-31c' to each side of the equation. -36a + 31c + -31c = 27b + -31c Combine like terms: 31c + -31c = 0 -36a + 0 = 27b + -31c -36a = 27b + -31c Divide each side by '-36'. a = -0.75b + 0.8611111111c Simplifying a = -0.75b + 0.8611111111c
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