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Simplifying 8(2b + c + -6a) + -4(a + -3c + 6b) = 0 Reorder the terms: 8(-6a + 2b + c) + -4(a + -3c + 6b) = 0 (-6a * 8 + 2b * 8 + c * 8) + -4(a + -3c + 6b) = 0 (-48a + 16b + 8c) + -4(a + -3c + 6b) = 0 Reorder the terms: -48a + 16b + 8c + -4(a + 6b + -3c) = 0 -48a + 16b + 8c + (a * -4 + 6b * -4 + -3c * -4) = 0 -48a + 16b + 8c + (-4a + -24b + 12c) = 0 Reorder the terms: -48a + -4a + 16b + -24b + 8c + 12c = 0 Combine like terms: -48a + -4a = -52a -52a + 16b + -24b + 8c + 12c = 0 Combine like terms: 16b + -24b = -8b -52a + -8b + 8c + 12c = 0 Combine like terms: 8c + 12c = 20c -52a + -8b + 20c = 0 Solving -52a + -8b + 20c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8b' to each side of the equation. -52a + -8b + 8b + 20c = 0 + 8b Combine like terms: -8b + 8b = 0 -52a + 0 + 20c = 0 + 8b -52a + 20c = 0 + 8b Remove the zero: -52a + 20c = 8b Add '-20c' to each side of the equation. -52a + 20c + -20c = 8b + -20c Combine like terms: 20c + -20c = 0 -52a + 0 = 8b + -20c -52a = 8b + -20c Divide each side by '-52'. a = -0.1538461538b + 0.3846153846c Simplifying a = -0.1538461538b + 0.3846153846c
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