Answer
$x=\left\{ -1,\dfrac{6}{5} \right\}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the Distributive Property, the given expression, $
(x-1)(5x+4)=2
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(5x)+x(4)-1(5x)-1(4)=2
\\\\
5x^2+4x-5x-4=2
\\\\
5x^2+4x-5x-4-2=0
\\\\
5x^2-x-6=0
.\end{array}
Factoring the above equation, $
5x^2-x-6=0
,$ results to
\begin{array}{l}\require{cancel}
(5x-6)(x+1)=0
.\end{array}
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
(5x-6)(x+1)=0
,$ are
\begin{array}{l}\require{cancel}
5x-6=0
\\\\
5x=6
\\\\
x=\dfrac{6}{5}
,\\\\\text{OR}\\\\
x+1=0
\\\\
x=-1
.\end{array}
Hence, $
x=\left\{ -1,\dfrac{6}{5} \right\}
.$
