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Simplifying 12(1 + -3g) + 8(g + -1f) = 0 (1 * 12 + -3g * 12) + 8(g + -1f) = 0 (12 + -36g) + 8(g + -1f) = 0 Reorder the terms: 12 + -36g + 8(-1f + g) = 0 12 + -36g + (-1f * 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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