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Simplifying 12p + 5pd + -3p + 6(pd + 2p) = 0 12p + 5dp + -3p + (dp * 6 + 2p * 6) = 0 12p + 5dp + -3p + (6dp + 12p) = 0 Reorder the terms: 5dp + 6dp + 12p + -3p + 12p = 0 Combine like terms: 5dp + 6dp = 11dp 11dp + 12p + -3p + 12p = 0 Combine like terms: 12p + -3p = 9p 11dp + 9p + 12p = 0 Combine like terms: 9p + 12p = 21p 11dp + 21p = 0 Solving 11dp + 21p = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-21p' to each side of the equation. 11dp + 21p + -21p = 0 + -21p Combine like terms: 21p + -21p = 0 11dp + 0 = 0 + -21p 11dp = 0 + -21p Remove the zero: 11dp = -21p Divide each side by '11p'. d = -1.909090909 Simplifying d = -1.909090909
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