(i-6)(i+4)=100

Solution for (i-6)(i+4)=100 equation:

Simplifying
(i + -6)(i + 4) = 100

Reorder the terms:
(-6 + i)(i + 4) = 100

Reorder the terms:
(-6 + i)(4 + i) = 100

Multiply (-6 + i) * (4 + i)
(-6(4 + i) + i(4 + i)) = 100
((4 * -6 + i * -6) + i(4 + i)) = 100
((-24 + -6i) + i(4 + i)) = 100
(-24 + -6i + (4 * i + i * i)) = 100
(-24 + -6i + (4i + i2)) = 100

Combine like terms: -6i + 4i = -2i
(-24 + -2i + i2) = 100

Solving
-24 + -2i + i2 = 100

Solving for variable 'i'.

Reorder the terms:
-24 + -100 + -2i + i2 = 100 + -100

Combine like terms: -24 + -100 = -124
-124 + -2i + i2 = 100 + -100

Combine like terms: 100 + -100 = 0
-124 + -2i + i2 = 0

Begin completing the square.

Move the constant term to the right:

Add '124' to each side of the equation.
-124 + -2i + 124 + i2 = 0 + 124

Reorder the terms:
-124 + 124 + -2i + i2 = 0 + 124

Combine like terms: -124 + 124 = 0
0 + -2i + i2 = 0 + 124
-2i + i2 = 0 + 124

Combine like terms: 0 + 124 = 124
-2i + i2 = 124

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 = 124 + 1

Reorder the terms:
1 + -2i + i2 = 124 + 1

Combine like terms: 124 + 1 = 125
1 + -2i + i2 = 125

Factor a perfect square on the left side:
(i + -1)(i + -1) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(i + -1) equal to 11.180339887 and -11.180339887.

Subproblem 1
i + -1 = 11.180339887

Simplifying
i + -1 = 11.180339887

Reorder the terms:
-1 + i = 11.180339887

Solving
-1 + i = 11.180339887

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 = 11.180339887 + 1

Combine like terms: -1 + 1 = 0
0 + i = 11.180339887 + 1
i = 11.180339887 + 1

Combine like terms: 11.180339887 + 1 = 12.180339887
i = 12.180339887

Simplifying
i = 12.180339887

Subproblem 2
i + -1 = -11.180339887

Simplifying
i + -1 = -11.180339887

Reorder the terms:
-1 + i = -11.180339887

Solving
-1 + i = -11.180339887

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 = -11.180339887 + 1

Combine like terms: -1 + 1 = 0
0 + i = -11.180339887 + 1
i = -11.180339887 + 1

Combine like terms: -11.180339887 + 1 = -10.180339887
i = -10.180339887

Simplifying
i = -10.180339887

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {12.180339887, -10.180339887}