-3(5+4i)-(8i)(5+i)=

Solution for -3(5+4i)-(8i)(5+i)= equation:

Simplifying
-3(5 + 4i) + -1(8i)(5 + i) = 0
(5 * -3 + 4i * -3) + -1(8i)(5 + i) = 0
(-15 + -12i) + -1(8i)(5 + i) = 0

Remove parenthesis around (8i)
-15 + -12i + -1 * 8i(5 + i) = 0

Multiply -1 * 8
-15 + -12i + -8i(5 + i) = 0
-15 + -12i + (5 * -8i + i * -8i) = 0
-15 + -12i + (-40i + -8i2) = 0

Combine like terms: -12i + -40i = -52i
-15 + -52i + -8i2 = 0

Solving
-15 + -52i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 52i + 8i2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(15 + 52i + 8i2)' equal to zero and attempt to solve:

Simplifying
15 + 52i + 8i2 = 0

Solving
15 + 52i + 8i2 = 0

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

Divide each side by '8'.
1.875 + 6.5i + i2 = 0

Move the constant term to the right:

Add '-1.875' to each side of the equation.
1.875 + 6.5i + -1.875 + i2 = 0 + -1.875

Reorder the terms:
1.875 + -1.875 + 6.5i + i2 = 0 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + 6.5i + i2 = 0 + -1.875
6.5i + i2 = 0 + -1.875

Combine like terms: 0 + -1.875 = -1.875
6.5i + i2 = -1.875

The i term is 6.5i.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5i + 10.5625 + i2 = -1.875 + 10.5625

Reorder the terms:
10.5625 + 6.5i + i2 = -1.875 + 10.5625

Combine like terms: -1.875 + 10.5625 = 8.6875
10.5625 + 6.5i + i2 = 8.6875

Factor a perfect square on the left side:
(i + 3.25)(i + 3.25) = 8.6875

Calculate the square root of the right side: 2.947456531

Break this problem into two subproblems by setting 
(i + 3.25) equal to 2.947456531 and -2.947456531.

Subproblem 1
i + 3.25 = 2.947456531

Simplifying
i + 3.25 = 2.947456531

Reorder the terms:
3.25 + i = 2.947456531

Solving
3.25 + i = 2.947456531

Solving for variable 'i'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + i = 2.947456531 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + i = 2.947456531 + -3.25
i = 2.947456531 + -3.25

Combine like terms: 2.947456531 + -3.25 = -0.302543469
i = -0.302543469

Simplifying
i = -0.302543469

Subproblem 2
i + 3.25 = -2.947456531

Simplifying
i + 3.25 = -2.947456531

Reorder the terms:
3.25 + i = -2.947456531

Solving
3.25 + i = -2.947456531

Solving for variable 'i'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + i = -2.947456531 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + i = -2.947456531 + -3.25
i = -2.947456531 + -3.25

Combine like terms: -2.947456531 + -3.25 = -6.197456531
i = -6.197456531

Simplifying
i = -6.197456531

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {-0.302543469, -6.197456531}
Solution
i = {-0.302543469, -6.197456531}