How do you solve an equation?

Lets say that the equation is: 2+3x+2x=22

1. 2+5x=22 Combine Like Terms.
2. 2-2+5x=22-2 Subtract 2 from each side.
3. 5x=20 Simplify.
4. 5x/5=20/5 Divide 5 on each side.
5. x=4 Simplify.

Check...

1. 2+3x+2x=22 x=4
2. 2+3(4)+2(4)=22 Substitute x for 4.
3. 2+12+8=22 Multiply and Divide first from left to right.
4. 14+8=22 Add and Subtract from left to right.
5. 22=22

Should you have an equation with higher order (like x2) then different methods, like factoring or the quadratic formula will apply.
Eh?