The next few problems present a sequence of typical equations and ask you to solve them. You need to understand the techniques involved and gain facility in using them. So you should do these problems by hand rather than use an advanced calculator or a symbol manipulation language like Maple. I recommend you enter answers as exact arithmetic expressions rather than decimal approximations. So, for example, type 3/7 instead of 0.42857 or sqrt(3)/2 instead of 0.86602.

The solution of the equation $$(x-1)(x-2) = (x+2)(x-3)$$ is $x=$ .
Hint: Expand on both sides, collect everything on one side, and solve the resulting linear equation.