Solve equation: p^3+8p^2=18p

Question

I can't seem to figure out how to solve this equation. I guess the first step to move the 18p so p^3+8p^2-18p=0 then pull out a p for p(p^2+8p-18) but then what?

Answer 1

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.