Stationary Point after Partial Differentiation

[ZedCar]

Homework Statement

A question in a book has partially differentiated a function

f(x,y) = x^2 + 8xy^2 + 2y^2

df/dx = 2x + 8y^2 = 0 at stationary point (eqn 1)
df/dy = 16xy + 4y = 0 at stationary point (eqn 2)

Homework Equations

The Attempt at a Solution

It then states;

From (eqn 2) either
y = 0, or 16x + 4 = 0
y = 0, or x = -1/4

I can understand how y=0, but how do they conclude that 16x + 4 = 0

Thank you

 

[ZedCar]

I've realized they've just factored out the y!