Answer
$-2x(3x-7)(5x+2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
-30x^3+58x^2+28x
,$ factor first the negative $GCF.$ Then find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
Factoring the negative $GCF=
-2x
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-2x(15x^2-29x-14)
.\end{array}
Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $
15(-14)=-210
$ and the value of $b$ is $
-29
.$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{
-35,6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-2x(15x^2-35x+6x-14)
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
-2x[(15x^2-35x)+(6x-14)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-2x[5x(3x-7)+2(3x-7)]
.\end{array}
Factoring the $GCF=
(3x-7)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-2x[(3x-7)(5x+2)]
\\\\=
-2x(3x-7)(5x+2)
.\end{array}