Diophantus problem

Question

I was given following problem as an example of early mathematics with the solutions. But it seems i can't understand from where they are getting the 35z^2 = 5 from in the solutions. Could someone please example what was the step done on that part? Thanks.

Answer 1

Since $(35z^3 -2z)^3 = (3z)^3$, we take cube roots.

This gives us $35z^3 -2z = 3z$, at which point the result is immediate.