Solve (m+4)x^2<2(mx-m+3)

$$( m + 4 ) x ^ { 2 } < 2 ( m x - m + 3 )$$

Solve for x

$$\left\{\begin{matrix}x\neq 3\text{, }&m=-6\\x\in \mathrm{R}\text{, }&m<-6\\x\in \left(-\frac{\sqrt{\left(4-m\right)\left(m+6\right)}-m}{m+4},\frac{\sqrt{\left(4-m\right)\left(m+6\right)}+m}{m+4}\right)\text{, }&|m|<4\\x<\frac{7}{4}\text{, }&m=-4\\x\in \left(-\infty,\frac{\sqrt{\left(4-m\right)\left(m+6\right)}+m}{m+4}\right)\cup \left(-\frac{\sqrt{\left(4-m\right)\left(m+6\right)}-m}{m+4},\infty\right)\text{, }&m>-6\text{ and }m<-4\end{matrix}\right.$$

Solve for m

$$m<-\frac{2\left(2x^{2}-3\right)}{x^{2}-2x+2}$$