(5-2i)-2(3+i)=0

Solution for (5-2i)-2(3+i)=0 equation:

Simplifying
(5 + -2i) + -2(3 + i) = 0

Remove parenthesis around (5 + -2i)
5 + -2i + -2(3 + i) = 0
5 + -2i + (3 * -2 + i * -2) = 0
5 + -2i + (-6 + -2i) = 0

Reorder the terms:
5 + -6 + -2i + -2i = 0

Combine like terms: 5 + -6 = -1
-1 + -2i + -2i = 0

Combine like terms: -2i + -2i = -4i
-1 + -4i = 0

Solving
-1 + -4i = 0

Solving for variable 'i'.

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

Add '1' to each side of the equation.
-1 + 1 + -4i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4i = 0 + 1
-4i = 0 + 1

Combine like terms: 0 + 1 = 1
-4i = 1

Divide each side by '-4'.
i = -0.25

Simplifying
i = -0.25