2(6+5i)-(2+1i)(3+6i)=

Solution for 2(6+5i)-(2+1i)(3+6i)= equation:

Simplifying
2(6 + 5i) + -1(2 + 1i)(3 + 6i) = 0
(6 * 2 + 5i * 2) + -1(2 + 1i)(3 + 6i) = 0
(12 + 10i) + -1(2 + 1i)(3 + 6i) = 0

Multiply (2 + 1i) * (3 + 6i)
12 + 10i + -1(2(3 + 6i) + 1i * (3 + 6i)) = 0
12 + 10i + -1((3 * 2 + 6i * 2) + 1i * (3 + 6i)) = 0
12 + 10i + -1((6 + 12i) + 1i * (3 + 6i)) = 0
12 + 10i + -1(6 + 12i + (3 * 1i + 6i * 1i)) = 0
12 + 10i + -1(6 + 12i + (3i + 6i2)) = 0

Combine like terms: 12i + 3i = 15i
12 + 10i + -1(6 + 15i + 6i2) = 0
12 + 10i + (6 * -1 + 15i * -1 + 6i2 * -1) = 0
12 + 10i + (-6 + -15i + -6i2) = 0

Reorder the terms:
12 + -6 + 10i + -15i + -6i2 = 0

Combine like terms: 12 + -6 = 6
6 + 10i + -15i + -6i2 = 0

Combine like terms: 10i + -15i = -5i
6 + -5i + -6i2 = 0

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

Solving for variable 'i'.

Factor a trinomial.
(2 + -3i)(3 + 2i) = 0

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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve:

Simplifying
3 + 2i = 0

Solving
3 + 2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Solution
i = {0.6666666667, -1.5}