Solve 8bx^2-5ax=0

$$8 b x ^ { 2 } - 5 a x = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=\frac{8bx}{5}\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 8bx^{2} from both sides. Anything subtracted from zero gives its negation.

$$-5ax=-8bx^{2}$$

The equation is in standard form.

$$\left(-5x\right)a=-8bx^{2}$$

Divide both sides by -5x.

$$\frac{\left(-5x\right)a}{-5x}=-\frac{8bx^{2}}{-5x}$$

Dividing by -5x undoes the multiplication by -5x.

$$a=-\frac{8bx^{2}}{-5x}$$

Divide -8bx^{2} by -5x.

$$a=\frac{8bx}{5}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{5a}{8x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 5ax to both sides. Anything plus zero gives itself.

$$8bx^{2}=5ax$$

The equation is in standard form.

$$8x^{2}b=5ax$$

Divide both sides by 8x^{2}.

$$\frac{8x^{2}b}{8x^{2}}=\frac{5ax}{8x^{2}}$$

Dividing by 8x^{2} undoes the multiplication by 8x^{2}.

$$b=\frac{5ax}{8x^{2}}$$

Divide 5ax by 8x^{2}.

$$b=\frac{5a}{8x}$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{8bx}{5}\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 8bx^{2} from both sides. Anything subtracted from zero gives its negation.

$$-5ax=-8bx^{2}$$

The equation is in standard form.

$$\left(-5x\right)a=-8bx^{2}$$

Divide both sides by -5x.

$$\frac{\left(-5x\right)a}{-5x}=-\frac{8bx^{2}}{-5x}$$

Dividing by -5x undoes the multiplication by -5x.

$$a=-\frac{8bx^{2}}{-5x}$$

Divide -8bx^{2} by -5x.

$$a=\frac{8bx}{5}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{5a}{8x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 5ax to both sides. Anything plus zero gives itself.

$$8bx^{2}=5ax$$

The equation is in standard form.

$$8x^{2}b=5ax$$

Divide both sides by 8x^{2}.

$$\frac{8x^{2}b}{8x^{2}}=\frac{5ax}{8x^{2}}$$

Dividing by 8x^{2} undoes the multiplication by 8x^{2}.

$$b=\frac{5ax}{8x^{2}}$$

Divide 5ax by 8x^{2}.

$$b=\frac{5a}{8x}$$