Q10: Since both absolute values equal each other, there are two possibilities: $x^2-11x+10=2x^2+x-45$, or $x^2-11x+10=-(2x^2+x-45)$. Both are quadratic equations and you should know how to solve them.
Q11: No squares are negative, and no absolute values are negative. This equation means a non-negative number equals a non-positive number. Therefore, both sides have to be $0$. From there you can figure out the values of $m$ and $n$.
Q12: Remove the absolute values, one layer at a time. The first step: two cases: either $11-|11-|11-2x||=2$ or $11-|11-|11-2x||=-2$. In each case, simplify and get the next layer.
Q13: First make a change of variable: $y=x^2+x+1$.