In a technical workshop on algebraic modeling, you are tasked with solving the equation ${}3c^2 = 10c - 8$ using the factoring method. Arrange the following steps in the correct order to find the values of $c$.

An operations analyst in a logistics company is using the quadratic model ${}3c^2 = 10c - 8$ to determine the optimal number of cargo containers ($c$) for a shipment. According to the factoring method, after rewriting the equation in standard form as ${}3c^2 - 10c + 8 = 0$, what is the correct factored form of the expression used to solve for $c$?

A production supervisor uses the quadratic equation ${}3c^2 = 10c - 8$ to determine an efficiency coefficient $c$ for a manufacturing process. True or False: When solving this equation using the factoring method, the two resulting linear equations derived from the Zero Product Property are ${}3c - 4 = 0$ and $c - 2 = 0$.

A facilities manager at a regional airport is using the quadratic model ${}3c^2 = 10c - 8$ to calculate the required width ($c$) of a drainage channel. To solve for $c$ using the factoring method, the manager must navigate through several key algebraic forms. Match each stage of the solution process with its correct mathematical representation.

Inventory Planning Equation Forms

A supply chain analyst is evaluating a warehouse space optimization model given by the quadratic equation ${}3c^2 = 10c - 8$, where $c$ represents a clearance ratio. To solve for $c$ by factoring, the analyst first writes the equation in standard form as ${}3c^2 - 10c + 8 = 0$ and then factors it into $(3c - 4)(c - 2) = 0$. Using the Zero Product Property, the analyst determines there are two possible solutions. The whole number solution for the clearance ratio $c$ is ____.

Capacity Planning Solver Documentation