Solve for p:
40 p^3 - 8 p^2 + 5 p - 1 = 0
The left hand side factors into a product with two terms:
(5 p - 1) (8 p^2 + 1) = 0
Split into two equations:
5 p - 1 = 0 or 8 p^2 + 1 = 0
Add 1 to both sides:
5 p = 1 or 8 p^2 + 1 = 0
Divide both sides by 5:
p = 1/5 or 8 p^2 + 1 = 0
Subtract 1 from both sides:
p = 1/5 or 8 p^2 = -1
Divide both sides by 8:
p = 1/5 or p^2 = -1/8
Take the square root of both sides:
Answer: | | p = 1/5 or p = i/(2 sqrt(2)) or p = -i/(2 sqrt(2))