-2(3+13i)+3i(7-2i)=

Solution for -2(3+13i)+3i(7-2i)= equation:

Simplifying
-2(3 + 13i) + 3i(7 + -2i) = 0
(3 * -2 + 13i * -2) + 3i(7 + -2i) = 0
(-6 + -26i) + 3i(7 + -2i) = 0
-6 + -26i + (7 * 3i + -2i * 3i) = 0
-6 + -26i + (21i + -6i2) = 0

Combine like terms: -26i + 21i = -5i
-6 + -5i + -6i2 = 0

Solving
-6 + -5i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5i + 6i2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 5i + 6i2)' equal to zero and attempt to solve:

Simplifying
6 + 5i + 6i2 = 0

Solving
6 + 5i + 6i2 = 0

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

Divide each side by '6'.
1 + 0.8333333333i + i2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.8333333333i + -1 + i2 = 0 + -1

Reorder the terms:
1 + -1 + 0.8333333333i + i2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.8333333333i + i2 = 0 + -1
0.8333333333i + i2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.8333333333i + i2 = -1

The i term is 0.8333333333i.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333i + 0.1736111111 + i2 = -1 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333i + i2 = -1 + 0.1736111111

Combine like terms: -1 + 0.1736111111 = -0.8263888889
0.1736111111 + 0.8333333333i + i2 = -0.8263888889

Factor a perfect square on the left side:
(i + 0.4166666667)(i + 0.4166666667) = -0.8263888889

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.