[z-4i]+[z+2i]=10

Solution for [z-4i]+[z+2i]=10 equation:

Simplifying
[z + -4i] + [z + 2i] = 10

Reorder the terms:
[-4i + z] + [z + 2i] = 10

Remove brackets around [-4i + z]
-4i + z + [z + 2i] = 10

Reorder the terms:
-4i + z + [2i + z] = 10

Remove brackets around [2i + z]
-4i + z + 2i + z = 10

Reorder the terms:
-4i + 2i + z + z = 10

Combine like terms: -4i + 2i = -2i
-2i + z + z = 10

Combine like terms: z + z = 2z
-2i + 2z = 10

Solving
-2i + 2z = 10

Solving for variable 'i'.

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

Add '-2z' to each side of the equation.
-2i + 2z + -2z = 10 + -2z

Combine like terms: 2z + -2z = 0
-2i + 0 = 10 + -2z
-2i = 10 + -2z

Divide each side by '-2'.
i = -5 + z

Simplifying
i = -5 + z