Rearranging formulae (change of subject)

When squaring both sides or moving terms across, signs get dropped or flipped, or only one term of a side is squared.

Leaving the subject in two places and getting stuck; the key step of factorising it out to isolate it is missed.

Cancelling a letter that is added, not a factor of the whole side. Only a common factor of the entire side may be cancelled — you cannot cancel the $x$ in $\dfrac{x+3}{x}$.

When freeing a squared subject, root the whole side: $v^2=u^2+2as$ gives $u=\sqrt{v^2-2as}$, not $u=v-\sqrt{2as}$. Square or root the entire side, never term by term.

After isolating the subject you must divide everything on the other side by its coefficient, e.g. from $x(y-1)=3+2y$ divide the whole right side to get $x=\dfrac{3+2y}{y-1}$.