<s>[INST] 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? 
 [/INST] $$ 3 = -x^2 +4x \implies \ x^2 -4x+3 = 0$$
$$ x^2 - 3x - x +3 = 0$$
$$ x(x-3)-1(x-3)$$
$$ (x-3)(x-1) = 0$$
$$x = 1, x = 3$$
For more on the methods, visit this link.
Alternatively, you could use the quadratic formula:
$$x =  \frac{-b \pm\sqrt{b^2 - 4ac}}{2a}$$
This was obtained from the quadratic equation:
$$ax^2 + bx +c = 0$$
where $a = 1, b = -4, c = 3$
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