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Simplifying 8e + f + 6g + -5g + 3f + -2e = 0 Reorder the terms: 8e + -2e + f + 3f + 6g + -5g = 0 Combine like terms: 8e + -2e = 6e 6e + f + 3f + 6g + -5g = 0 Combine like terms: f + 3f = 4f 6e + 4f + 6g + -5g = 0 Combine like terms: 6g + -5g = 1g 6e + 4f + 1g = 0 Solving 6e + 4f + 1g = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-4f' to each side of the equation. 6e + 4f + -4f + 1g = 0 + -4f Combine like terms: 4f + -4f = 0 6e + 0 + 1g = 0 + -4f 6e + 1g = 0 + -4f Remove the zero: 6e + 1g = -4f Add '-1g' to each side of the equation. 6e + 1g + -1g = -4f + -1g Combine like terms: 1g + -1g = 0 6e + 0 = -4f + -1g 6e = -4f + -1g Divide each side by '6'. e = -0.6666666667f + -0.1666666667g Simplifying e = -0.6666666667f + -0.1666666667g
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