Solve lambda=L+Mb^2/M*b

$$\lambda = \frac { L + M b ^ { 2 } } { M \cdot b }$$

Solve for M

$$\left\{\begin{matrix}M=\frac{L}{b\left(\lambda -b\right)}\text{, }&L\neq 0\text{ and }b\neq 0\text{ and }\lambda \neq b\\M\neq 0\text{, }&L=0\text{ and }\lambda =b\text{ and }b\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Mb.

$$\lambda Mb=L+Mb^{2}$$

Subtract Mb^{2} from both sides.

$$\lambda Mb-Mb^{2}=L$$

Reorder the terms.

$$-Mb^{2}+Mb\lambda =L$$

Combine all terms containing M.

$$\left(-b^{2}+b\lambda \right)M=L$$

The equation is in standard form.

$$\left(b\lambda -b^{2}\right)M=L$$

Divide both sides by \lambda b-b^{2}.

$$\frac{\left(b\lambda -b^{2}\right)M}{b\lambda -b^{2}}=\frac{L}{b\lambda -b^{2}}$$

Dividing by \lambda b-b^{2} undoes the multiplication by \lambda b-b^{2}.

$$M=\frac{L}{b\lambda -b^{2}}$$

Divide L by \lambda b-b^{2}.

$$M=\frac{L}{b\left(\lambda -b\right)}$$

Variable M cannot be equal to 0.

$$M=\frac{L}{b\left(\lambda -b\right)}\text{, }M\neq 0$$

Solve for L

$$L=-Mb\left(b-\lambda \right)$$

$$M\neq 0\text{ and }b\neq 0$$