#### Answer

$m=1$ and $m=\dfrac{5}{2}$

#### Work Step by Step

$(m+2)(2m-6)=5(m-1)-12$
Evaluate the products present on both sides of the equation:
$2m^{2}-2m-12=5m-5-12$
Take all terms to the left side of the equation:
$2m^{2}-2m-12-5m+5+12=0$
Simplify the equation by combining like terms:
$2m^{2}-7m+5=0$
Use the quadratic formula to solve the resulting equation. The formula is $m=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=-7$ and $c=5$
Substitute:
$m=\dfrac{-(-7)\pm\sqrt{(-7)^{2}-4(2)(5)}}{2(2)}=\dfrac{7\pm\sqrt{49-40}}{4}=...$
$...=\dfrac{7\pm\sqrt{9}}{4}=\dfrac{7\pm3}{4}$
Our two solutions are:
$m=\dfrac{7-3}{4}=1$
$m=\dfrac{7+3}{4}=\dfrac{5}{2}$