Xiao Li uses the mathematical idea of substitution to solve the equation: $(x^2+1)^2+4(x^2+1)-5=0$. He treats $(x^2+1)$ as a whole and sets $x^2+1=y$ ($y>0$), then the original equation can be transformed into $y^2+4y-5=0$, solving this yields $y_1=1$, $y_2=-5$ (which is discarded as it does not meet the condition). When $y=1$, $x^2+1=1$, thus $x^2=0$, therefore $x=0$. Hence, the solution to the original equation is $x=0$. Please use this mathematical idea to solve the following problem:
In $\triangle ABC$, $\angle C=90°$, the lengths of the two legs are $a$ and $b$, and the length of the hypotenuse is $c$, given that $(a^2+b^2)(a^2+b^2+1)=12$, find the length of the hypotenuse $c$.