Let's have some hint on these problems.

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: $y=x^2+x+1$.