(6+4i)(1+2i)=

Solution for (6+4i)(1+2i)= equation:

Simplifying
(6 + 4i)(1 + 2i) = 0

Multiply (6 + 4i) * (1 + 2i)
(6(1 + 2i) + 4i * (1 + 2i)) = 0
((1 * 6 + 2i * 6) + 4i * (1 + 2i)) = 0
((6 + 12i) + 4i * (1 + 2i)) = 0
(6 + 12i + (1 * 4i + 2i * 4i)) = 0
(6 + 12i + (4i + 8i2)) = 0

Combine like terms: 12i + 4i = 16i
(6 + 16i + 8i2) = 0

Solving
6 + 16i + 8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 8i + 4i2) = 0

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

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

Simplifying
1 + 2i = 0

Solving
1 + 2i = 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 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Solution
i = {-1.5, -0.5}