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Simplifying 6(3f + -4g) + -1(2g + -1f) = 0 (3f * 6 + -4g * 6) + -1(2g + -1f) = 0 (18f + -24g) + -1(2g + -1f) = 0 Reorder the terms: 18f + -24g + -1(-1f + 2g) = 0 18f + -24g + (-1f * -1 + 2g * -1) = 0 18f + -24g + (1f + -2g) = 0 Reorder the terms: 18f + 1f + -24g + -2g = 0 Combine like terms: 18f + 1f = 19f 19f + -24g + -2g = 0 Combine like terms: -24g + -2g = -26g 19f + -26g = 0 Solving 19f + -26g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '26g' to each side of the equation. 19f + -26g + 26g = 0 + 26g Combine like terms: -26g + 26g = 0 19f + 0 = 0 + 26g 19f = 0 + 26g Remove the zero: 19f = 26g Divide each side by '19'. f = 1.368421053g Simplifying f = 1.368421053g
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