Answer
$x=\left\{ -\dfrac{13}{5},0,2 \right\}$
Work Step by Step
The factored form of the given expression, $
x^2(5x+3)=26x
$, is
\begin{array}{l}
5x^3+3x^2-26x=0
\\\\
x(5x^2+3x-26)=0
\\\\
x(5x+13)(x-2)=0
.\end{array}
Equating each factor to zero, then
\begin{array}{l}
x=0
,\text{ OR}\\\\
5x+13=0
\\
5x=0-13
\\
5x=-13
\\
x=-\dfrac{13}{5}
,\text{ OR}\\\\
x-2=0
\\
x=0+2
\\
x=2
\end{array}
Hence, $
x=\left\{ -\dfrac{13}{5},0,2 \right\}
$.
