solve the following quadratic equation and show steps

2z^4 +14z^3 + 20z^2

I don't see an equation to solve.

did you mean 2z^4 +14z^3 + 20z^2 = 0 ?
if so, then

2z^2 (z^2 + 7z + 10) = 0
z^2 (z+5)(z+2) = 0
z = 0 , -5 , -2