A quality control technician uses the quadratic equation $(3x - 8)(x - 1) = 3x$ to model the stability of a production line. To find the specific settings $x$ where the line is stable, the technician must solve the equation.

Arrange the following steps in the correct order to solve for $x$ based on the standard algebraic solution method.

A project coordinator is solving the equation $(3x - 8)(x - 1) = 3x$ to determine the number of workdays required for a phase of a construction project. After expanding the binomials on the left, the coordinator must move all terms to one side to reach the standard quadratic form $ax^2 + bx + c = 0$. Which of the following is the correct standard form for this equation?

A manufacturing analyst is solving the equation $(3x - 8)(x - 1) = 3x$ to find the break-even points for a new component. To document the process clearly for a manager, the analyst identifies the key stages of the solution. Match each algebraic description with the corresponding expression used during the solving process.

A commercial HVAC technician is solving the equation $(3x - 8)(x - 1) = 3x$ to determine system pressure. To use the Zero Product Property, the technician must first rewrite the equation in standard form. True or False: The correct standard form for this specific equation is ${}3x^2 - 14x + 8 = 0$.

Modeling Unit Costs with Quadratic Equations

A supply chain analyst is solving the equation $(3x - 8)(x - 1) = 3x$ to determine the optimal number of weekly shipments. After factoring the standard quadratic form to $(3x - 2)(x - 4) = 0$, the analyst sets each individual factor equal to zero (${}3x - 2 = 0$ and $x - 4 = 0$) to solve for $x$. This specific mathematical rule used to separate the factors is called the ____ Property.

Recalling Key Algebraic Properties in Inventory Modeling