Answer
$x=\left\{ -\dfrac{5}{2},7 \right\}$
Work Step by Step
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
4x^2-18x=70
\\\\
4x^2-18x-70=0
\\\\
\dfrac{4x^2-18x-70}{2}=\dfrac{0}{2}
\\\\
2x^2-9x-35=0
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given $\text{
equation
}$
\begin{array}{l}\require{cancel}
2x^2-9x-35=0
\end{array} has $ac=
2(-35)=-70
$ and $b=
-9
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-14,5
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2x^2-14x+5x-35=0
.\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^2-14x)+(5x-35)=0
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2x(x-7)+5(x-7)=0
.\end{array}
Factoring the $GCF=
(x-7)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x-7)(2x+5)=0
.\end{array}
Equating each factor to zero (Zero Product Property), and then isolating the variable, the solutions are $
x=\left\{ -\dfrac{5}{2},7 \right\}
.$
