#### Answer

$m=\left\{ -\dfrac{2}{5},1 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given eqution, $
5m(m-1)=2(1-m)
,$ express the equation in the form $ax^2+bx+c=0.$ Then express the equation in factored form. Next step is to equate each factor to zero (Zero Product Property). Finally, solve each equation.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac$ and then combining like terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
5m^2-5m=2-2m
\\\\
5m^2+(-5m+2m)-2=0
\\\\
5m^2-3m-2=0
.\end{array}
Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $
5(-2)=-10
$ and the value of $b$ is $
-3
.$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{
2,-5
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
5m^2+2m-5m-2=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}
(5m^2+2m)-(5m+2)=0
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
m(5m+2)-(5m+2)=0
.\end{array}
Factoring the $GCF=
(5m+2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5m+2)(m-1)=0
.\end{array}
Equating each factor to zero (Zero Product Property), the solutions to the equation above are
\begin{array}{l}\require{cancel}
5m+2=0
\\\\\text{OR}\\\\
m-1=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5m+2=0
\\\\
5m=-2
\\\\
m=-\dfrac{2}{5}
\\\\\text{OR}\\\\
m-1=0
\\\\
m=1
.\end{array}
Hence, $
m=\left\{ -\dfrac{2}{5},1 \right\}
.$