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Simplifying 11d + 5f + 21d + 5 + 8 = 0 Reorder the terms: 5 + 8 + 11d + 21d + 5f = 0 Combine like terms: 5 + 8 = 13 13 + 11d + 21d + 5f = 0 Combine like terms: 11d + 21d = 32d 13 + 32d + 5f = 0 Solving 13 + 32d + 5f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + 32d + -13 + 5f = 0 + -13 Reorder the terms: 13 + -13 + 32d + 5f = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 32d + 5f = 0 + -13 32d + 5f = 0 + -13 Combine like terms: 0 + -13 = -13 32d + 5f = -13 Add '-5f' to each side of the equation. 32d + 5f + -5f = -13 + -5f Combine like terms: 5f + -5f = 0 32d + 0 = -13 + -5f 32d = -13 + -5f Divide each side by '32'. d = -0.40625 + -0.15625f Simplifying d = -0.40625 + -0.15625f
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