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Simplifying 21d + 5f + -11d + 9 + -8 = 0 Reorder the terms: 9 + -8 + 21d + -11d + 5f = 0 Combine like terms: 9 + -8 = 1 1 + 21d + -11d + 5f = 0 Combine like terms: 21d + -11d = 10d 1 + 10d + 5f = 0 Solving 1 + 10d + 5f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 10d + -1 + 5f = 0 + -1 Reorder the terms: 1 + -1 + 10d + 5f = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10d + 5f = 0 + -1 10d + 5f = 0 + -1 Combine like terms: 0 + -1 = -1 10d + 5f = -1 Add '-5f' to each side of the equation. 10d + 5f + -5f = -1 + -5f Combine like terms: 5f + -5f = 0 10d + 0 = -1 + -5f 10d = -1 + -5f Divide each side by '10'. d = -0.1 + -0.5f Simplifying d = -0.1 + -0.5f
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