Final answer:
The expression the student has provided is not a quadratic equation; it is an unsimplified algebraic expression with no immediate common factors between terms. The details regarding the quadratic formula and the cubing of exponentials are unrelated to the simplification of this algebraic expression.
Step-by-step explanation:
The expression provided by the student is an algebraic expression involving variables with exponents and coefficients. It is not a quadratic equation and does not fit the form at² + bt + c = 0. For the process of simplifying such expressions, we look for common factors or use algebraic identities. Specifically, to simplify -24a³b³c³ - 84a⁴b²c, we can search for a common factor that can be factored out from both terms. However, without additional context or specific instructions to combine or simplify certain variables, we must keep the terms separate as part of the simplification process.
Regarding the miscopied content about quadratic equations and the quadratic formula, those details do not apply to the given algebraic expression. Nonetheless, the process of solving a quadratic equation using the quadratic formula involves substituting the respective values of a, b, and c into the formula -b ± √(b² - 4ac) over 2a and calculating the result to find the solutions for the variable t.