Yes, it can be written p(p2+8p-18)=0.
p=0 is one solution. Now solve the quadratic:
p2+8p=18,
p2+8p+16=18+16,
(p+4)2=34,
p+4=±√34,
p=-4+√34, -4-√34.
Three roots: 0, -4+√34, -4-√34. This can be approximately evaluated by using √34=5.83095:
x=0, 1.83095, -9.83095.