5i(-3+6i)=0

Solution for 5i(-3+6i)=0 equation:

Simplifying
5i(-3 + 6i) = 0
(-3 * 5i + 6i * 5i) = 0
(-15i + 30i2) = 0

Solving
-15i + 30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '15i'.
15i(-1 + 2i) = 0

Ignore the factor 15.
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}