Solve (z+i)(z-3i)=z(z-i)

$$( z + i ) ( z - 3 i ) = z ( z - i )$$

Solve for z

$$z=-3i$$

Steps for Solving Linear Equation

Use the distributive property to multiply z+i by z-3i and combine like terms.

$$z^{2}-2iz+3=z\left(z-i\right)$$

Use the distributive property to multiply z by z-i.

$$z^{2}-2iz+3=z^{2}-iz$$

Subtract z^{2} from both sides.

$$z^{2}-2iz+3-z^{2}=-iz$$

Combine z^{2} and -z^{2} to get 0.

$$-2iz+3=-iz$$

Subtract -iz from both sides.

$$-2iz+3-\left(-iz\right)=0$$

Combine -2iz and iz to get -iz.

$$-iz+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-iz=-3$$

Divide both sides by -i.

$$z=\frac{-3}{-i}$$

Multiply both numerator and denominator of \frac{-3}{-i} by imaginary unit i.

$$z=\frac{-3i}{1}$$

Divide -3i by 1 to get -3i.

$$z=-3i$$