Solve x^2+2a^2=(2b+3a)x-2ab

$$x ^ { 2 } + 2 a ^ { 2 } = ( 2 b + 3 a ) x - 2 a b$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=\frac{x-2a}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2b+3a by x.

$$x^{2}+2a^{2}=2bx+3ax-2ab$$

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

$$2bx+3ax-2ab=x^{2}+2a^{2}$$

Subtract 3ax from both sides.

$$2bx-2ab=x^{2}+2a^{2}-3ax$$

Combine all terms containing b.

$$\left(2x-2a\right)b=x^{2}+2a^{2}-3ax$$

The equation is in standard form.

$$\left(2x-2a\right)b=x^{2}-3ax+2a^{2}$$

Divide both sides by 2x-2a.

$$\frac{\left(2x-2a\right)b}{2x-2a}=\frac{\left(x-a\right)\left(x-2a\right)}{2x-2a}$$

Dividing by 2x-2a undoes the multiplication by 2x-2a.

$$b=\frac{\left(x-a\right)\left(x-2a\right)}{2x-2a}$$

Divide \left(x-2a\right)\left(x-a\right) by 2x-2a.

$$b=\frac{x}{2}-a$$

Solve for b

$$\left\{\begin{matrix}\\b=\frac{x-2a}{2}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=a\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2b+3a by x.

$$x^{2}+2a^{2}=2bx+3ax-2ab$$

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

$$2bx+3ax-2ab=x^{2}+2a^{2}$$

Subtract 3ax from both sides.

$$2bx-2ab=x^{2}+2a^{2}-3ax$$

Combine all terms containing b.

$$\left(2x-2a\right)b=x^{2}+2a^{2}-3ax$$

The equation is in standard form.

$$\left(2x-2a\right)b=x^{2}-3ax+2a^{2}$$

Divide both sides by 2x-2a.

$$\frac{\left(2x-2a\right)b}{2x-2a}=\frac{\left(x-a\right)\left(x-2a\right)}{2x-2a}$$

Dividing by 2x-2a undoes the multiplication by 2x-2a.

$$b=\frac{\left(x-a\right)\left(x-2a\right)}{2x-2a}$$

Divide \left(x-2a\right)\left(x-a\right) by 2x-2a.

$$b=\frac{x}{2}-a$$

Solve for a

$$a=x$$

$$a=\frac{x-2b}{2}$$