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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 = -3 -3 + 11d + -21d + 5f = 0 Combine like terms: 11d + -21d = -10d -3 + -10d + 5f = 0 Solving -3 + -10d + 5f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -10d + 3 + 5f = 0 + 3 Reorder the terms: -3 + 3 + -10d + 5f = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10d + 5f = 0 + 3 -10d + 5f = 0 + 3 Combine like terms: 0 + 3 = 3 -10d + 5f = 3 Add '-5f' to each side of the equation. -10d + 5f + -5f = 3 + -5f Combine like terms: 5f + -5f = 0 -10d + 0 = 3 + -5f -10d = 3 + -5f Divide each side by '-10'. d = -0.3 + 0.5f Simplifying d = -0.3 + 0.5f
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