Literal Equation
A literal equation is an equation that contains two or more variables (letters), such as a formula that can be rearranged to solve for any one variable.
Definition
A literal equation is an equation with more than one variable (letter); formulas are literal equations, and you can rearrange them to solve for any variable you want by using the same inverse-operation techniques as with numerical equations, treating all other variables as if they were constants. When you solve a literal equation for a specific variable, the goal is not a number but an expression, since the variable you solved for becomes defined in terms of the others. Formally, a literal equation is a polynomial (or rational) identity in multiple indeterminates, solved for one indeterminate in terms of the others; in the context of implicit differentiation, a two-variable equation $F(x, y) = 0$ can be solved for $dy/dx = -(dF/dx)/(dF/dy)$ by the implicit function theorem, provided $dF/dy \neq 0$.
Example
The perimeter formula $P = 2l + 2w$ has three variables; solving for $l$ means subtracting $2w$ from both sides and dividing by $2$, giving $l = (P-2w)/2$. Solve $d = rt$ for $t$: divide both sides by $r$ to get $t = d/r$. Rearranging the ideal gas law $PV = nRT$ for $T$ gives $T = PV/(nR)$, expressing $T$ as a rational function of $P$, $V$, $n$, and $R$, with the restriction $nR \neq 0$.
Key Insight
Every formula you use in science and math is a literal equation, and rearranging formulas is a key skill for real-world problem solving. The implicit function theorem generalizes the rearrangement of literal equations to nonlinear settings: near a point where $dF/dy \neq 0$, a curve $F(x, y) = 0$ locally defines $y$ as a smooth function of $x$.