2(3-7i)-i(-4+5i)=

Solution for 2(3-7i)-i(-4+5i)= equation:

Simplifying
2(3 + -7i) + -1i(-4 + 5i) = 0
(3 * 2 + -7i * 2) + -1i(-4 + 5i) = 0
(6 + -14i) + -1i(-4 + 5i) = 0
6 + -14i + (-4 * -1i + 5i * -1i) = 0
6 + -14i + (4i + -5i2) = 0

Combine like terms: -14i + 4i = -10i
6 + -10i + -5i2 = 0

Solving
6 + -10i + -5i2 = 0

Solving for variable 'i'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + 2i + i2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 2i + 1.2 + i2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 2i + i2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 2i + i2 = 0 + 1.2
2i + i2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
2i + i2 = 1.2

The i term is 2i.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2i + 1 + i2 = 1.2 + 1

Reorder the terms:
1 + 2i + i2 = 1.2 + 1

Combine like terms: 1.2 + 1 = 2.2
1 + 2i + i2 = 2.2

Factor a perfect square on the left side:
(i + 1)(i + 1) = 2.2

Calculate the square root of the right side: 1.483239697

Break this problem into two subproblems by setting 
(i + 1) equal to 1.483239697 and -1.483239697.

Subproblem 1
i + 1 = 1.483239697

Simplifying
i + 1 = 1.483239697

Reorder the terms:
1 + i = 1.483239697

Solving
1 + i = 1.483239697

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 + i = 1.483239697 + -1

Combine like terms: 1 + -1 = 0
0 + i = 1.483239697 + -1
i = 1.483239697 + -1

Combine like terms: 1.483239697 + -1 = 0.483239697
i = 0.483239697

Simplifying
i = 0.483239697

Subproblem 2
i + 1 = -1.483239697

Simplifying
i + 1 = -1.483239697

Reorder the terms:
1 + i = -1.483239697

Solving
1 + i = -1.483239697

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 + i = -1.483239697 + -1

Combine like terms: 1 + -1 = 0
0 + i = -1.483239697 + -1
i = -1.483239697 + -1

Combine like terms: -1.483239697 + -1 = -2.483239697
i = -2.483239697

Simplifying
i = -2.483239697

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {0.483239697, -2.483239697}