Solve (m)(r-1)(r+3)=5(r+3)

$$( m ) ( r - 1 ) ( r + 3 ) = 5 ( r + 3 )$$

Solve for m

$$\left\{\begin{matrix}m=\frac{5}{r-1}\text{, }&r\neq 1\\m\in \mathrm{R}\text{, }&r=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by r-1.

$$\left(mr-m\right)\left(r+3\right)=5\left(r+3\right)$$

Use the distributive property to multiply mr-m by r+3 and combine like terms.

$$mr^{2}+2mr-3m=5\left(r+3\right)$$

Use the distributive property to multiply 5 by r+3.

$$mr^{2}+2mr-3m=5r+15$$

Combine all terms containing m.

$$\left(r^{2}+2r-3\right)m=5r+15$$

Divide both sides by r^{2}+2r-3.

$$\frac{\left(r^{2}+2r-3\right)m}{r^{2}+2r-3}=\frac{5r+15}{r^{2}+2r-3}$$

Dividing by r^{2}+2r-3 undoes the multiplication by r^{2}+2r-3.

$$m=\frac{5r+15}{r^{2}+2r-3}$$

Divide 15+5r by r^{2}+2r-3.

$$m=\frac{5}{r-1}$$

Solve for r

$$\left\{\begin{matrix}\\r=-3\text{, }&\text{unconditionally}\\r=\frac{m+5}{m}\text{, }&m\neq 0\end{matrix}\right.$$