A manufacturing technician is analyzing a material stress model where the equilibrium points are defined by the equation ${}16y^2 = 32y^3 + 2y$. Arrange the following steps in the correct chronological order to solve this equation for $y$ using the factoring method.

A quality control analyst is solving the equation ${}16y^2 = 32y^3 + 2y$ to determine the equilibrium points of a precision milling machine. After rewriting the equation in the standard form ${}32y^3 - 16y^2 + 2y = 0$, what is the Greatest Common Factor (GCF) that must be factored out from all three terms?

A technical analyst is evaluating a component's stability using the model equation ${}16y^2 = 32y^3 + 2y$. To document the solution process for the quality control manual, match each mathematical component with its corresponding role or result in the solving process.

A shop foreman is using the mathematical model ${}16y^2 = 32y^3 + 2y$ to calculate the optimal speed for a conveyor belt. True or False: After solving this equation by factoring and using the Zero Product Property, the foreman determines that the two distinct values for the speed $y$ are $y = 0$ and y = rac{1}{4}.

A materials testing technician is modeling the flex point $y$ (in inches) of a new polymer using the equation ${}16y^2 = 32y^3 + 2y$. After rearranging the equation to ${}32y^3 - 16y^2 + 2y = 0$ and completely factoring it to ${}2y(4y - 1)^2 = 0$, the technician applies the Zero Product Property. The two distinct solutions for the flex point $y$ are ${}0$ and ____.