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Simplifying (6e + 9y + -12f) + -1(8e + 56g + 12f) = 0 Reorder the terms: (6e + -12f + 9y) + -1(8e + 56g + 12f) = 0 Remove parenthesis around (6e + -12f + 9y) 6e + -12f + 9y + -1(8e + 56g + 12f) = 0 Reorder the terms: 6e + -12f + 9y + -1(8e + 12f + 56g) = 0 6e + -12f + 9y + (8e * -1 + 12f * -1 + 56g * -1) = 0 6e + -12f + 9y + (-8e + -12f + -56g) = 0 Reorder the terms: 6e + -8e + -12f + -12f + -56g + 9y = 0 Combine like terms: 6e + -8e = -2e -2e + -12f + -12f + -56g + 9y = 0 Combine like terms: -12f + -12f = -24f -2e + -24f + -56g + 9y = 0 Solving -2e + -24f + -56g + 9y = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '24f' to each side of the equation. -2e + -24f + -56g + 24f + 9y = 0 + 24f Reorder the terms: -2e + -24f + 24f + -56g + 9y = 0 + 24f Combine like terms: -24f + 24f = 0 -2e + 0 + -56g + 9y = 0 + 24f -2e + -56g + 9y = 0 + 24f Remove the zero: -2e + -56g + 9y = 24f Add '56g' to each side of the equation. -2e + -56g + 56g + 9y = 24f + 56g Combine like terms: -56g + 56g = 0 -2e + 0 + 9y = 24f + 56g -2e + 9y = 24f + 56g Add '-9y' to each side of the equation. -2e + 9y + -9y = 24f + 56g + -9y Combine like terms: 9y + -9y = 0 -2e + 0 = 24f + 56g + -9y -2e = 24f + 56g + -9y Divide each side by '-2'. e = -12f + -28g + 4.5y Simplifying e = -12f + -28g + 4.5y
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