Solve x^2-2ax=6ab-3bx

$$x ^ { 2 } - 2 a x = 6 a b - 3 b x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{x}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=-3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6ab from both sides.

$$x^{2}-2ax-6ab=-3bx$$

Subtract x^{2} from both sides.

$$-2ax-6ab=-3bx-x^{2}$$

Combine all terms containing a.

$$\left(-2x-6b\right)a=-3bx-x^{2}$$

The equation is in standard form.

$$\left(-2x-6b\right)a=-x^{2}-3bx$$

Divide both sides by -2x-6b.

$$\frac{\left(-2x-6b\right)a}{-2x-6b}=-\frac{x\left(x+3b\right)}{-2x-6b}$$

Dividing by -2x-6b undoes the multiplication by -2x-6b.

$$a=-\frac{x\left(x+3b\right)}{-2x-6b}$$

Divide -x\left(3b+x\right) by -2x-6b.

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

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=-\frac{x}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=2a\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$6ab-3bx=x^{2}-2ax$$

Combine all terms containing b.

$$\left(6a-3x\right)b=x^{2}-2ax$$

Divide both sides by 6a-3x.

$$\frac{\left(6a-3x\right)b}{6a-3x}=\frac{x\left(x-2a\right)}{6a-3x}$$

Dividing by 6a-3x undoes the multiplication by 6a-3x.

$$b=\frac{x\left(x-2a\right)}{6a-3x}$$

Divide x\left(x-2a\right) by 6a-3x.

$$b=-\frac{x}{3}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{x}{2}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=-3b\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6ab from both sides.

$$x^{2}-2ax-6ab=-3bx$$

Subtract x^{2} from both sides.

$$-2ax-6ab=-3bx-x^{2}$$

Combine all terms containing a.

$$\left(-2x-6b\right)a=-3bx-x^{2}$$

The equation is in standard form.

$$\left(-2x-6b\right)a=-x^{2}-3bx$$

Divide both sides by -2x-6b.

$$\frac{\left(-2x-6b\right)a}{-2x-6b}=-\frac{x\left(x+3b\right)}{-2x-6b}$$

Dividing by -2x-6b undoes the multiplication by -2x-6b.

$$a=-\frac{x\left(x+3b\right)}{-2x-6b}$$

Divide -x\left(3b+x\right) by -2x-6b.

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

Solve for b

$$\left\{\begin{matrix}\\b=-\frac{x}{3}\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=2a\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$6ab-3bx=x^{2}-2ax$$

Combine all terms containing b.

$$\left(6a-3x\right)b=x^{2}-2ax$$

Divide both sides by 6a-3x.

$$\frac{\left(6a-3x\right)b}{6a-3x}=\frac{x\left(x-2a\right)}{6a-3x}$$

Dividing by 6a-3x undoes the multiplication by 6a-3x.

$$b=\frac{x\left(x-2a\right)}{6a-3x}$$

Divide x\left(x-2a\right) by 6a-3x.

$$b=-\frac{x}{3}$$