Solve L=(P+1)M+P*S

$$L = ( P + 1 ) M + P \cdot S$$

Solve for M

$$\left\{\begin{matrix}M=-\frac{PS-L}{P+1}\text{, }&P\neq -1\\M\in \mathrm{R}\text{, }&L=-S\text{ and }P=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply P+1 by M.

$$L=PM+M+PS$$

Swap sides so that all variable terms are on the left hand side.

$$PM+M+PS=L$$

Subtract PS from both sides.

$$PM+M=L-PS$$

Combine all terms containing M.

$$\left(P+1\right)M=L-PS$$

Divide both sides by P+1.

$$\frac{\left(P+1\right)M}{P+1}=\frac{L-PS}{P+1}$$

Dividing by P+1 undoes the multiplication by P+1.

$$M=\frac{L-PS}{P+1}$$

Solve for L

$$L=MP+M+PS$$