When is it most appropriate to use completing the square method to solve a quadratic equation?

It's best to use the completing the square method to solve a quadratic when the coefficient of the squared term is 1 and the coefficient of the linear term is even.

step-by-step explanation:

in the absence of parentheses, i will have to make some assumptions:   i interpret your (3x+5/y^6)(4y^3/5)​ to mean:

3x + 5     4y^(3/5)       (3x + 5)(4)

* =

    y^6             1               y^(6-3/5)

if this is not what you expected, repost your question using parentheses to indicate whether you meant

4y^3

    or   4y^(3/5)

    5

y=mx+b is the final answer!   : )