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Simplifying (12f + -3r) + -1(6f + 5s) + -1(8s + -8) = 0 Remove parenthesis around (12f + -3r) 12f + -3r + -1(6f + 5s) + -1(8s + -8) = 0 12f + -3r + (6f * -1 + 5s * -1) + -1(8s + -8) = 0 12f + -3r + (-6f + -5s) + -1(8s + -8) = 0 Reorder the terms: 12f + -3r + -6f + -5s + -1(-8 + 8s) = 0 12f + -3r + -6f + -5s + (-8 * -1 + 8s * -1) = 0 12f + -3r + -6f + -5s + (8 + -8s) = 0 Reorder the terms: 8 + 12f + -6f + -3r + -5s + -8s = 0 Combine like terms: 12f + -6f = 6f 8 + 6f + -3r + -5s + -8s = 0 Combine like terms: -5s + -8s = -13s 8 + 6f + -3r + -13s = 0 Solving 8 + 6f + -3r + -13s = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 6f + -3r + -8 + -13s = 0 + -8 Reorder the terms: 8 + -8 + 6f + -3r + -13s = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 6f + -3r + -13s = 0 + -8 6f + -3r + -13s = 0 + -8 Combine like terms: 0 + -8 = -8 6f + -3r + -13s = -8 Add '3r' to each side of the equation. 6f + -3r + 3r + -13s = -8 + 3r Combine like terms: -3r + 3r = 0 6f + 0 + -13s = -8 + 3r 6f + -13s = -8 + 3r Add '13s' to each side of the equation. 6f + -13s + 13s = -8 + 3r + 13s Combine like terms: -13s + 13s = 0 6f + 0 = -8 + 3r + 13s 6f = -8 + 3r + 13s Divide each side by '6'. f = -1.333333333 + 0.5r + 2.166666667s Simplifying f = -1.333333333 + 0.5r + 2.166666667s
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