Models & Qualitative Behavior · Challenge problem

In the reaction $A + B \to C$, the concentration $x$ (in mol/L) of product satisfies $x' = (2 - x)(3 - x)$, with $t$ in seconds and $x(0) = 0$ (initially $2$ mol/L of $A$ and $3$ mol/L of $B$). How many seconds does it take to produce $1$ mol/L of $C$? Give an exact answer.