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Simplifying 8k + -7d + 3f + -21 = -9w + 12d + -1f Reorder the terms: -21 + -7d + 3f + 8k = -9w + 12d + -1f Reorder the terms: -21 + -7d + 3f + 8k = 12d + -1f + -9w Solving -21 + -7d + 3f + 8k = 12d + -1f + -9w Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12d' to each side of the equation. -21 + -7d + 3f + -12d + 8k = 12d + -1f + -12d + -9w Reorder the terms: -21 + -7d + -12d + 3f + 8k = 12d + -1f + -12d + -9w Combine like terms: -7d + -12d = -19d -21 + -19d + 3f + 8k = 12d + -1f + -12d + -9w Reorder the terms: -21 + -19d + 3f + 8k = 12d + -12d + -1f + -9w Combine like terms: 12d + -12d = 0 -21 + -19d + 3f + 8k = 0 + -1f + -9w -21 + -19d + 3f + 8k = -1f + -9w Add '21' to each side of the equation. -21 + -19d + 3f + 21 + 8k = -1f + 21 + -9w Reorder the terms: -21 + 21 + -19d + 3f + 8k = -1f + 21 + -9w Combine like terms: -21 + 21 = 0 0 + -19d + 3f + 8k = -1f + 21 + -9w -19d + 3f + 8k = -1f + 21 + -9w Reorder the terms: -19d + 3f + 8k = 21 + -1f + -9w Add '-3f' to each side of the equation. -19d + 3f + -3f + 8k = 21 + -1f + -3f + -9w Combine like terms: 3f + -3f = 0 -19d + 0 + 8k = 21 + -1f + -3f + -9w -19d + 8k = 21 + -1f + -3f + -9w Combine like terms: -1f + -3f = -4f -19d + 8k = 21 + -4f + -9w Add '-8k' to each side of the equation. -19d + 8k + -8k = 21 + -4f + -8k + -9w Combine like terms: 8k + -8k = 0 -19d + 0 = 21 + -4f + -8k + -9w -19d = 21 + -4f + -8k + -9w Divide each side by '-19'. d = -1.105263158 + 0.2105263158f + 0.4210526316k + 0.4736842105w Simplifying d = -1.105263158 + 0.2105263158f + 0.4210526316k + 0.4736842105w
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