Answer
$\left\{ 1,\dfrac{5}{2} \right\}$
Work Step by Step
The standard form of the given equation, $
(m+2)(2m-6)=5(m-1)-12
,$ is
\begin{array}{l}\require{cancel}
m(2m)+m(-6)+2(2m)+2(-6)=5(m)+5(-1)-12
\\\\
2m^2-6m+4m-12=5m-5-12
\\\\
2m^2-2m-12=5m-17
\\\\
2m^2+(-2m-5m)+(-12+17)=0
\\\\
2m^2-7m+5=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
2m^2-7m+5=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(5)}}{2(2)}
\\\\=
\dfrac{7\pm\sqrt{49-40}}{4}
\\\\=
\dfrac{7\pm\sqrt{9}}{4}
\\\\=
\dfrac{7\pm\sqrt{(3)^2}}{4}
\\\\=
\dfrac{7\pm3}{4}
\\\\=
\dfrac{7-3}{4}
\text{ OR }
\dfrac{7+3}{4}
\\\\=
\dfrac{4}{4}
\text{ OR }
\dfrac{10}{4}
\\\\=
1
\text{ OR }
\dfrac{5}{2}
.\end{array}
Hence, the solutions are $
\left\{ 1,\dfrac{5}{2} \right\}
.$
