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

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

Simplifying
(-6 + 2i)(2 + 3i) = 0

Multiply (-6 + 2i) * (2 + 3i)
(-6(2 + 3i) + 2i * (2 + 3i)) = 0
((2 * -6 + 3i * -6) + 2i * (2 + 3i)) = 0
((-12 + -18i) + 2i * (2 + 3i)) = 0
(-12 + -18i + (2 * 2i + 3i * 2i)) = 0
(-12 + -18i + (4i + 6i2)) = 0

Combine like terms: -18i + 4i = -14i
(-12 + -14i + 6i2) = 0

Solving
-12 + -14i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7i + 3i2) = 0

Factor a trinomial.
2((-2 + -3i)(3 + -1i)) = 0

Ignore the factor 2.
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 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 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 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {-0.6666666667, 3}