Solve $3 = -x^2+4x$ by factoring I have $3 = -x^2 + 4x$ and I need to solve it by factoring. According to wolframalpha the solution is $x_1 = 1, x_2 = 3$.
\begin{align*}
 3 & = -x^2 + 4x\\
 x^2-4x+3 & = 0
\end{align*}
According to wolframalpha $(x-3) (x-1) = 0$ is the equation factored, which allows me to solve it, but how do I get to this step? 

Solving by factoring means reducing the polynomial to a lower degree by dividing it by factors $(x-x_i)$ for already known roots $x_i$.
The reason for this is that the lower degree polynomial might be easier to solve. Here this is not necessary, as a order $2$ polynomial is already solvable with moderate effort.
How to know roots? For this kind of task one should always try the $0, \pm 1, \pm 2$, which here gives $x_1 = 1$. 
What is left is the division:
\begin{align}
& x^2 - 4x + 3 : x - 1 = x - 3 \\
-&(x^2-x) \\
= & -3x+3 = -3(x-1)
\end{align}
So we have the factored polynomial $(x+1)(x-3)$.
