Solve l=2(a+b)[a]

$$l = 2 ( a + b ) [ a ]$$

Solve for b

$$\left\{\begin{matrix}b=-a+\frac{l}{2a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&l=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by a+b.

$$l=\left(2a+2b\right)a$$

Use the distributive property to multiply 2a+2b by a.

$$l=2a^{2}+2ba$$

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

$$2a^{2}+2ba=l$$

Subtract 2a^{2} from both sides.

$$2ba=l-2a^{2}$$

The equation is in standard form.

$$2ab=l-2a^{2}$$

Divide both sides by 2a.

$$\frac{2ab}{2a}=\frac{l-2a^{2}}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$b=\frac{l-2a^{2}}{2a}$$

Divide l-2a^{2} by 2a.

$$b=-a+\frac{l}{2a}$$

Solve for a

$$a=\frac{\sqrt{b^{2}+2l}-b}{2}$$

$$a=\frac{-\sqrt{b^{2}+2l}-b}{2}\text{, }l\geq -\frac{b^{2}}{2}$$