Solve 6+15iz-7i=0

$$6 + 15 i z - 7 i = 0$$

Solve for z

$$z=\frac{7}{15}+\frac{2}{5}i\approx 0.466666667+0.4i$$

Steps for Solving Linear Equation

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$15iz-7i=-6$$

Add 7i to both sides.

$$15iz=-6+7i$$

Divide both sides by 15i.

$$z=\frac{-6+7i}{15i}$$

Multiply both numerator and denominator of \frac{-6+7i}{15i} by imaginary unit i.

$$z=\frac{\left(-6+7i\right)i}{15i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$z=\frac{\left(-6+7i\right)i}{-15}$$

Multiply -6+7i times i.

$$z=\frac{-6i+7i^{2}}{-15}$$

By definition, i^{2} is -1.

$$z=\frac{-6i+7\left(-1\right)}{-15}$$

Do the multiplications in -6i+7\left(-1\right). Reorder the terms.

$$z=\frac{-7-6i}{-15}$$

Divide -7-6i by -15 to get \frac{7}{15}+\frac{2}{5}i.

$$z=\frac{7}{15}+\frac{2}{5}i$$