3+3i(8-2i)-7=

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Solution for 3+3i(8-2i)-7= equation: 


Simplifying
3 + 3i(8 + -2i) + -7 = 0
3 + (8 * 3i + -2i * 3i) + -7 = 0
3 + (24i + -6i2) + -7 = 0

Reorder the terms:
3 + -7 + 24i + -6i2 = 0

Combine like terms: 3 + -7 = -4
-4 + 24i + -6i2 = 0

Solving
-4 + 24i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 12i + -3i2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 12i + -3i2)' equal to zero and attempt to solve:

Simplifying
-2 + 12i + -3i2 = 0

Solving
-2 + 12i + -3i2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.6666666667 + -4i + i2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -4i + -0.6666666667 + i2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -4i + i2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -4i + i2 = 0 + -0.6666666667
-4i + i2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-4i + i2 = -0.6666666667

The i term is -4i.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4i + 4 + i2 = -0.6666666667 + 4

Reorder the terms:
4 + -4i + i2 = -0.6666666667 + 4

Combine like terms: -0.6666666667 + 4 = 3.3333333333
4 + -4i + i2 = 3.3333333333

Factor a perfect square on the left side:
(i + -2)(i + -2) = 3.3333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(i + -2) equal to 1.825741858 and -1.825741858.


Subproblem 1
i + -2 = 1.825741858

Simplifying
i + -2 = 1.825741858

Reorder the terms:
-2 + i = 1.825741858

Solving
-2 + i = 1.825741858

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 2 + i = 1.825741858 + 2

Combine like terms: -2 + 2 = 0
0 + i = 1.825741858 + 2
i = 1.825741858 + 2

Combine like terms: 1.825741858 + 2 = 3.825741858
i = 3.825741858

Simplifying
i = 3.825741858


Subproblem 2
i + -2 = -1.825741858

Simplifying
i + -2 = -1.825741858

Reorder the terms:
-2 + i = -1.825741858

Solving
-2 + i = -1.825741858

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 2 + i = -1.825741858 + 2

Combine like terms: -2 + 2 = 0
0 + i = -1.825741858 + 2
i = -1.825741858 + 2

Combine like terms: -1.825741858 + 2 = 0.174258142
i = 0.174258142

Simplifying
i = 0.174258142


Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {3.825741858, 0.174258142}
Solution
i = {3.825741858, 0.174258142}

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