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Simplifying (12f + -3r) + -1(6f + 5s) + -1(8s + -8f) = 0 Remove parenthesis around (12f + -3r) 12f + -3r + -1(6f + 5s) + -1(8s + -8f) = 0 12f + -3r + (6f * -1 + 5s * -1) + -1(8s + -8f) = 0 12f + -3r + (-6f + -5s) + -1(8s + -8f) = 0 Reorder the terms: 12f + -3r + -6f + -5s + -1(-8f + 8s) = 0 12f + -3r + -6f + -5s + (-8f * -1 + 8s * -1) = 0 12f + -3r + -6f + -5s + (8f + -8s) = 0 Reorder the terms: 12f + -6f + 8f + -3r + -5s + -8s = 0 Combine like terms: 12f + -6f = 6f 6f + 8f + -3r + -5s + -8s = 0 Combine like terms: 6f + 8f = 14f 14f + -3r + -5s + -8s = 0 Combine like terms: -5s + -8s = -13s 14f + -3r + -13s = 0 Solving 14f + -3r + -13s = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '3r' to each side of the equation. 14f + -3r + 3r + -13s = 0 + 3r Combine like terms: -3r + 3r = 0 14f + 0 + -13s = 0 + 3r 14f + -13s = 0 + 3r Remove the zero: 14f + -13s = 3r Add '13s' to each side of the equation. 14f + -13s + 13s = 3r + 13s Combine like terms: -13s + 13s = 0 14f + 0 = 3r + 13s 14f = 3r + 13s Divide each side by '14'. f = 0.2142857143r + 0.9285714286s Simplifying f = 0.2142857143r + 0.9285714286s
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