Answer
$(5x-3)(4x+7)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
20x^2+23x-21
,$ factor first the $GCF.$ 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.
$\bf{\text{Solution Details:}}$
Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $
20(-21)=-240
$ and the value of $b$ is $
23
.$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{
-12,35
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
20x^2-12x+35x-21
.\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}
(20x^2-12x)+(35x-21)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
4x(5x-3)+7(5x-3)
.\end{array}
Factoring the $GCF=
(5x-3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5x-3)(4x+7)
.\end{array}
