Answer
$-2(2x-1)(x-3)$
Work Step by Step
Factoring the negative $GCF=
-2
,$ the given $\text{
expression
,}
-4x^2+14x-6
,$ is equivalent to
\begin{align*}
-2(2x^2-7x+3)
.\end{align*}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
-2(2x^2-7x+3)
\end{align*} has $ac=
2(3)=6
$ and $b=
-7
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-1,-6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
-2(2x^2-x-6x+3)
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{align*}
-2[(2x^2-x)-(6x-3)]
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
-2[x(2x-1)-3(2x-1)]
.\end{align*}
Factoring the $GCF=
(2x-1)
$ of the entire expression above results to
\begin{align*}
&
-2[(2x-1)(x-3)]
\\&=
-2(2x-1)(x-3)
.\end{align*}
