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Simplifying 24g + 3f + -1(2g + 6f) + -1(-3g + -1(2g + -8f) + 7g) = 0 Reorder the terms: 24g + 3f + -1(6f + 2g) + -1(-3g + -1(2g + -8f) + 7g) = 0 24g + 3f + (6f * -1 + 2g * -1) + -1(-3g + -1(2g + -8f) + 7g) = 0 24g + 3f + (-6f + -2g) + -1(-3g + -1(2g + -8f) + 7g) = 0 Reorder the terms: 24g + 3f + -6f + -2g + -1(-3g + -1(-8f + 2g) + 7g) = 0 24g + 3f + -6f + -2g + -1(-3g + (-8f * -1 + 2g * -1) + 7g) = 0 24g + 3f + -6f + -2g + -1(-3g + (8f + -2g) + 7g) = 0 Reorder the terms: 24g + 3f + -6f + -2g + -1(8f + -3g + -2g + 7g) = 0 Combine like terms: -3g + -2g = -5g 24g + 3f + -6f + -2g + -1(8f + -5g + 7g) = 0 Combine like terms: -5g + 7g = 2g 24g + 3f + -6f + -2g + -1(8f + 2g) = 0 24g + 3f + -6f + -2g + (8f * -1 + 2g * -1) = 0 24g + 3f + -6f + -2g + (-8f + -2g) = 0 Reorder the terms: 3f + -6f + -8f + 24g + -2g + -2g = 0 Combine like terms: 3f + -6f = -3f -3f + -8f + 24g + -2g + -2g = 0 Combine like terms: -3f + -8f = -11f -11f + 24g + -2g + -2g = 0 Combine like terms: 24g + -2g = 22g -11f + 22g + -2g = 0 Combine like terms: 22g + -2g = 20g -11f + 20g = 0 Solving -11f + 20g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-20g' to each side of the equation. -11f + 20g + -20g = 0 + -20g Combine like terms: 20g + -20g = 0 -11f + 0 = 0 + -20g -11f = 0 + -20g Remove the zero: -11f = -20g Divide each side by '-11'. f = 1.818181818g Simplifying f = 1.818181818g
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