(3+7i)(6-2i)=

Solution for (3+7i)(6-2i)= equation:

Simplifying
(3 + 7i)(6 + -2i) = 0

Multiply (3 + 7i) * (6 + -2i)
(3(6 + -2i) + 7i * (6 + -2i)) = 0
((6 * 3 + -2i * 3) + 7i * (6 + -2i)) = 0
((18 + -6i) + 7i * (6 + -2i)) = 0
(18 + -6i + (6 * 7i + -2i * 7i)) = 0
(18 + -6i + (42i + -14i2)) = 0

Combine like terms: -6i + 42i = 36i
(18 + 36i + -14i2) = 0

Solving
18 + 36i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 18i + -7i2) = 0

Factor a trinomial.
2((3 + -1i)(3 + 7i)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 7i)' equal to zero and attempt to solve:

Simplifying
3 + 7i = 0

Solving
3 + 7i = 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 + 7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7i = 0 + -3
7i = 0 + -3

Combine like terms: 0 + -3 = -3
7i = -3

Divide each side by '7'.
i = -0.4285714286

Simplifying
i = -0.4285714286
Solution
i = {3, -0.4285714286}