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Simplifying 3(4p + 1) + -9d = 6(2 + -1d) Reorder the terms: 3(1 + 4p) + -9d = 6(2 + -1d) (1 * 3 + 4p * 3) + -9d = 6(2 + -1d) (3 + 12p) + -9d = 6(2 + -1d) Reorder the terms: 3 + -9d + 12p = 6(2 + -1d) 3 + -9d + 12p = (2 * 6 + -1d * 6) 3 + -9d + 12p = (12 + -6d) Solving 3 + -9d + 12p = 12 + -6d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6d' to each side of the equation. 3 + -9d + 6d + 12p = 12 + -6d + 6d Combine like terms: -9d + 6d = -3d 3 + -3d + 12p = 12 + -6d + 6d Combine like terms: -6d + 6d = 0 3 + -3d + 12p = 12 + 0 3 + -3d + 12p = 12 Add '-3' to each side of the equation. 3 + -3d + -3 + 12p = 12 + -3 Reorder the terms: 3 + -3 + -3d + 12p = 12 + -3 Combine like terms: 3 + -3 = 0 0 + -3d + 12p = 12 + -3 -3d + 12p = 12 + -3 Combine like terms: 12 + -3 = 9 -3d + 12p = 9 Add '-12p' to each side of the equation. -3d + 12p + -12p = 9 + -12p Combine like terms: 12p + -12p = 0 -3d + 0 = 9 + -12p -3d = 9 + -12p Divide each side by '-3'. d = -3 + 4p Simplifying d = -3 + 4p
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