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Simplifying 12(1 + -3g) + 8(g + f) = 0 (1 * 12 + -3g * 12) + 8(g + f) = 0 (12 + -36g) + 8(g + f) = 0 Reorder the terms: 12 + -36g + 8(f + g) = 0 12 + -36g + (f * 8 + g * 8) = 0 12 + -36g + (8f + 8g) = 0 Reorder the terms: 12 + 8f + -36g + 8g = 0 Combine like terms: -36g + 8g = -28g 12 + 8f + -28g = 0 Solving 12 + 8f + -28g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 8f + -12 + -28g = 0 + -12 Reorder the terms: 12 + -12 + 8f + -28g = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 8f + -28g = 0 + -12 8f + -28g = 0 + -12 Combine like terms: 0 + -12 = -12 8f + -28g = -12 Add '28g' to each side of the equation. 8f + -28g + 28g = -12 + 28g Combine like terms: -28g + 28g = 0 8f + 0 = -12 + 28g 8f = -12 + 28g Divide each side by '8'. f = -1.5 + 3.5g Simplifying f = -1.5 + 3.5g
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