(i-3)6i-3(8-i)=

Solution for (i-3)6i-3(8-i)= equation:

Simplifying
(i + -3) * 6i + -3(8 + -1i) = 0

Reorder the terms:
(-3 + i) * 6i + -3(8 + -1i) = 0

Reorder the terms for easier multiplication:
6i(-3 + i) + -3(8 + -1i) = 0
(-3 * 6i + i * 6i) + -3(8 + -1i) = 0
(-18i + 6i2) + -3(8 + -1i) = 0
-18i + 6i2 + (8 * -3 + -1i * -3) = 0
-18i + 6i2 + (-24 + 3i) = 0

Reorder the terms:
-24 + -18i + 3i + 6i2 = 0

Combine like terms: -18i + 3i = -15i
-24 + -15i + 6i2 = 0

Solving
-24 + -15i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -5i + 2i2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -5i + 2i2)' equal to zero and attempt to solve:

Simplifying
-8 + -5i + 2i2 = 0

Solving
-8 + -5i + 2i2 = 0

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

Divide each side by '2'.
-4 + -2.5i + i2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.5i + 4 + i2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.5i + i2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.5i + i2 = 0 + 4
-2.5i + i2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.5i + i2 = 4

The i term is -2.5i.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5i + 1.5625 + i2 = 4 + 1.5625

Reorder the terms:
1.5625 + -2.5i + i2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + -2.5i + i2 = 5.5625

Factor a perfect square on the left side:
(i + -1.25)(i + -1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(i + -1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
i + -1.25 = 2.358495283

Simplifying
i + -1.25 = 2.358495283

Reorder the terms:
-1.25 + i = 2.358495283

Solving
-1.25 + i = 2.358495283

Solving for variable 'i'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + i = 2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + i = 2.358495283 + 1.25
i = 2.358495283 + 1.25

Combine like terms: 2.358495283 + 1.25 = 3.608495283
i = 3.608495283

Simplifying
i = 3.608495283

Subproblem 2
i + -1.25 = -2.358495283

Simplifying
i + -1.25 = -2.358495283

Reorder the terms:
-1.25 + i = -2.358495283

Solving
-1.25 + i = -2.358495283

Solving for variable 'i'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + i = -2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + i = -2.358495283 + 1.25
i = -2.358495283 + 1.25

Combine like terms: -2.358495283 + 1.25 = -1.108495283
i = -1.108495283

Simplifying
i = -1.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {3.608495283, -1.108495283}
Solution
i = {3.608495283, -1.108495283}