Verified answer

you're given

y^2 + 3yz - 8z - 4x = 0

factorize

z*(3y - 8) + y^2 - 4x = 0

z*(3y - 8) = 4x - y^2

z = (4x - y^2) / (3y - 8)

Bring all the Z to 1 side and u will get

y^2- 4x = 8z + 3yz

Then u take out z as the common factor

y^2- 4x = z

Divide 8+ 3y so as to solve for z

y^2- 4x/(8 + 3y) = z

z(3y-8)+y^2-4x=0

z(3y-8)=-y^2+4x

z=((-y^2+4x)/(3y-8))