p² (w₁₁ - 2w₁₂ + w₂₂) - p(w₁₁ - 2w₁₂ + w₂₂) + w₂₂ - w₁₂ = 0,

which yields,

Simplifying the above expression gives,

Because c ≠ 0 (we are given c > 0), we divide both sides by c and sort the terms in descending order (in p),

We eliminate the fractions by multiplying both sides by 2,

2p³ - 7p² + 7p -2 = 0.

Therefore, 2p³ - 7p² + 7p -2 = 0 is equivalent to,

p² (w₁₁ - 2w₁₂ + w₂₂) - p(w₁₁ - 2w₁₂ + w₂₂) + w₂₂ - w₁₂ = 0,

where w₁₁ = 1 - cp, w₁₂ = 1 - ½cp, and w₂₂ = 1 - c + cp.