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

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Add 3ax to both sides.

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

Subtract 3x^{2} from both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -3b+3x.

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

Dividing by -3b+3x undoes the multiplication by -3b+3x.

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

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

$$a=-x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract 3bx from both sides.

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

Subtract 3x^{2} from both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -3a-3x.

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

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

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

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

$$b=x$$

Solve for a

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

Steps for Solving Linear Equation

Add 3ax to both sides.

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

Subtract 3x^{2} from both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -3b+3x.

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

Dividing by -3b+3x undoes the multiplication by -3b+3x.

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

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

$$a=-x$$

Solve for b

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

Steps for Solving Linear Equation

Subtract 3bx from both sides.

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

Subtract 3x^{2} from both sides.

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

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -3a-3x.

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

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

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

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

$$b=x$$