(2-3i)(1-i)-(3-i)(3+i)=0

Solution for (2-3i)(1-i)-(3-i)(3+i)=0 equation:

Simplifying
(2 + -3i)(1 + -1i) + -1(3 + -1i)(3 + i) = 0

Multiply (2 + -3i) * (1 + -1i)
(2(1 + -1i) + -3i * (1 + -1i)) + -1(3 + -1i)(3 + i) = 0
((1 * 2 + -1i * 2) + -3i * (1 + -1i)) + -1(3 + -1i)(3 + i) = 0
((2 + -2i) + -3i * (1 + -1i)) + -1(3 + -1i)(3 + i) = 0
(2 + -2i + (1 * -3i + -1i * -3i)) + -1(3 + -1i)(3 + i) = 0
(2 + -2i + (-3i + 3i2)) + -1(3 + -1i)(3 + i) = 0

Combine like terms: -2i + -3i = -5i
(2 + -5i + 3i2) + -1(3 + -1i)(3 + i) = 0

Multiply (3 + -1i) * (3 + i)
2 + -5i + 3i2 + -1(3(3 + i) + -1i * (3 + i)) = 0
2 + -5i + 3i2 + -1((3 * 3 + i * 3) + -1i * (3 + i)) = 0
2 + -5i + 3i2 + -1((9 + 3i) + -1i * (3 + i)) = 0
2 + -5i + 3i2 + -1(9 + 3i + (3 * -1i + i * -1i)) = 0
2 + -5i + 3i2 + -1(9 + 3i + (-3i + -1i2)) = 0

Combine like terms: 3i + -3i = 0
2 + -5i + 3i2 + -1(9 + 0 + -1i2) = 0
2 + -5i + 3i2 + -1(9 + -1i2) = 0
2 + -5i + 3i2 + (9 * -1 + -1i2 * -1) = 0
2 + -5i + 3i2 + (-9 + 1i2) = 0

Reorder the terms:
2 + -9 + -5i + 3i2 + 1i2 = 0

Combine like terms: 2 + -9 = -7
-7 + -5i + 3i2 + 1i2 = 0

Combine like terms: 3i2 + 1i2 = 4i2
-7 + -5i + 4i2 = 0

Solving
-7 + -5i + 4i2 = 0

Solving for variable 'i'.

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

Divide each side by '4'.
-1.75 + -1.25i + i2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -1.25i + 1.75 + i2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -1.25i + i2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -1.25i + i2 = 0 + 1.75
-1.25i + i2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-1.25i + i2 = 1.75

The i term is -1.25i.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25i + 0.390625 + i2 = 1.75 + 0.390625

Reorder the terms:
0.390625 + -1.25i + i2 = 1.75 + 0.390625

Combine like terms: 1.75 + 0.390625 = 2.140625
0.390625 + -1.25i + i2 = 2.140625

Factor a perfect square on the left side:
(i + -0.625)(i + -0.625) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(i + -0.625) equal to 1.463087489 and -1.463087489.

Subproblem 1
i + -0.625 = 1.463087489

Simplifying
i + -0.625 = 1.463087489

Reorder the terms:
-0.625 + i = 1.463087489

Solving
-0.625 + i = 1.463087489

Solving for variable 'i'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + i = 1.463087489 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + i = 1.463087489 + 0.625
i = 1.463087489 + 0.625

Combine like terms: 1.463087489 + 0.625 = 2.088087489
i = 2.088087489

Simplifying
i = 2.088087489

Subproblem 2
i + -0.625 = -1.463087489

Simplifying
i + -0.625 = -1.463087489

Reorder the terms:
-0.625 + i = -1.463087489

Solving
-0.625 + i = -1.463087489

Solving for variable 'i'.

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

Add '0.625' to each side of the equation.
-0.625 + 0.625 + i = -1.463087489 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + i = -1.463087489 + 0.625
i = -1.463087489 + 0.625

Combine like terms: -1.463087489 + 0.625 = -0.838087489
i = -0.838087489

Simplifying
i = -0.838087489

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {2.088087489, -0.838087489}