1. **State the problem:** Solve for $x$ in the equation $5x = xc + 12$. 2. **Rewrite the equation:** The equation is $5x = xc + 12$. 3. **Isolate terms involving $x$:** Subtract $xc$ from both sides to get $5x - xc = 12$. 4. **Factor out $x$:** $x(5 - c) = 12$. 5. **Solve for $x$:** Divide both sides by $(5 - c)$, assuming $5 - c \neq 0$, to get $$x = \frac{12}{5 - c}$$ 6. **Conclusion:** The solution for $x$ is $x = \frac{12}{5 - c}$, provided $c \neq 5$ to avoid division by zero.