As a supply chain analyst, you are documenting the troubleshooting procedure for an inventory forecasting algorithm. The system flags an error when the batch parameter, $b$, satisfies the equation ${}123b = -6 - 60b^2$. To complete the standard operating procedure (SOP) documentation, recall the standard algebraic algorithm for solving quadratic equations and arrange the steps in the exact order required to manually calculate the error-triggering values of $b$.

A project analyst is using a resource optimization model governed by the equation ${}123b = -6 - 60b^2$, where $b$ represents a balance coefficient. According to the standard algebraic solution for this specific model, which of the following pairs of values represent the solutions for $b$?

A technical writer for an industrial equipment manual is documenting the procedure to solve for a machine's calibration constant $b$ using the equation ${}123b = -6 - 60b^2$. According to the standard algebraic solution, the equation is first rearranged into the standard form ${}60b^2 + 123b + 6 = 0$. The next step in the procedure is to factor out the greatest common factor (GCF). The value of this GCF is ____.

A junior systems analyst is updating the technical manual for a load-balancing algorithm governed by the equation ${}123b = -6 - 60b^2$. To ensure the documentation is accurate, match each stage of the solution process with its corresponding mathematical expression.

A quality control technician is documenting the calibration process for a system governed by the equation ${}123b = -6 - 60b^2$. After converting the equation to standard form and factoring out the greatest common factor, the technician reaches the step ${}3(20b^2 + 41b + 2) = 0$. According to the standard algebraic solution for this specific equation, is it true that the next step is to factor the expression into ${}3(20b + 1)(b + 2) = 0$?