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

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

Simplifying
(6 + 2i)(1 + -3i) = 0

Multiply (6 + 2i) * (1 + -3i)
(6(1 + -3i) + 2i * (1 + -3i)) = 0
((1 * 6 + -3i * 6) + 2i * (1 + -3i)) = 0
((6 + -18i) + 2i * (1 + -3i)) = 0
(6 + -18i + (1 * 2i + -3i * 2i)) = 0
(6 + -18i + (2i + -6i2)) = 0

Combine like terms: -18i + 2i = -16i
(6 + -16i + -6i2) = 0

Solving
6 + -16i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -8i + -3i2) = 0

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

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

Simplifying
1 + -3i = 0

Solving
1 + -3i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3i = 0 + -1

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

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

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Solution
i = {0.3333333333, -3}