(4-3i)*z=6+I

Solution for (4-3i)*z=6+I equation:

Simplifying
(4 + -3i) * z = 6 + I

Reorder the terms for easier multiplication:
z(4 + -3i) = 6 + I
(4 * z + -3i * z) = 6 + I

Reorder the terms:
(-3iz + 4z) = 6 + I
(-3iz + 4z) = 6 + I

Solving
-3iz + 4z = 6 + I

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-4z' to each side of the equation.
-3iz + 4z + -4z = 6 + I + -4z

Combine like terms: 4z + -4z = 0
-3iz + 0 = 6 + I + -4z
-3iz = 6 + I + -4z

Divide each side by '-3z'.
i = -2z-1 + -0.3333333333z-1I + 1.333333333

Simplifying
i = -2z-1 + -0.3333333333z-1I + 1.333333333

Reorder the terms:
i = 1.333333333 + -2z-1 + -0.3333333333z-1I