3i(1+2i)=

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

Simplifying
3i(1 + 2i) = 0
(1 * 3i + 2i * 3i) = 0
(3i + 6i2) = 0

Solving
3i + 6i2 = 0

Solving for variable 'i'.

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

Ignore the factor 3.
Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0
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 = {0, -0.5}