Solve 4i-4+z(5i-7)+z(9+6i)=0

$$4 i - 4 + z ( 5 i - 7 ) + z ( 9 + 6 i ) = 0$$

Solve for z

$$z=-\frac{36}{125}-\frac{52}{125}i=-0.288-0.416i$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 5i-7.

$$4i-4+5iz-7z+z\left(9+6i\right)=0$$

Combine 5iz and -7z to get \left(-7+5i\right)z.

$$4i-4+\left(-7+5i\right)z+z\left(9+6i\right)=0$$

Combine \left(-7+5i\right)z and z\left(9+6i\right) to get \left(2+11i\right)z.

$$4i-4+\left(2+11i\right)z=0$$

Subtract 4i from both sides. Anything subtracted from zero gives its negation.

$$-4+\left(2+11i\right)z=-4i$$

Add 4 to both sides.

$$\left(2+11i\right)z=-4i+4$$

The equation is in standard form.

$$\left(2+11i\right)z=4-4i$$

Divide both sides by 2+11i.

$$\frac{\left(2+11i\right)z}{2+11i}=\frac{4-4i}{2+11i}$$

Dividing by 2+11i undoes the multiplication by 2+11i.

$$z=\frac{4-4i}{2+11i}$$

Divide 4-4i by 2+11i.

$$z=-\frac{36}{125}-\frac{52}{125}i$$