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Simplifying 12e + 8f + 3g + -4e + -5f + -5g = 0 Reorder the terms: 12e + -4e + 8f + -5f + 3g + -5g = 0 Combine like terms: 12e + -4e = 8e 8e + 8f + -5f + 3g + -5g = 0 Combine like terms: 8f + -5f = 3f 8e + 3f + 3g + -5g = 0 Combine like terms: 3g + -5g = -2g 8e + 3f + -2g = 0 Solving 8e + 3f + -2g = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '-3f' to each side of the equation. 8e + 3f + -3f + -2g = 0 + -3f Combine like terms: 3f + -3f = 0 8e + 0 + -2g = 0 + -3f 8e + -2g = 0 + -3f Remove the zero: 8e + -2g = -3f Add '2g' to each side of the equation. 8e + -2g + 2g = -3f + 2g Combine like terms: -2g + 2g = 0 8e + 0 = -3f + 2g 8e = -3f + 2g Divide each side by '8'. e = -0.375f + 0.25g Simplifying e = -0.375f + 0.25g
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