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

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

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

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

Combine like terms: 6i + -2i = 4i
(6 + 4i + -2i2) = 0

Solving
6 + 4i + -2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2i + -1i2) = 0

Factor a trinomial.
2((3 + -1i)(1 + i)) = 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 '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
Solution
i = {3, -1}