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

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

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

Multiply (2 + -3i) * (1 + 2i)
(2(1 + 2i) + -3i * (1 + 2i)) = 0
((1 * 2 + 2i * 2) + -3i * (1 + 2i)) = 0
((2 + 4i) + -3i * (1 + 2i)) = 0
(2 + 4i + (1 * -3i + 2i * -3i)) = 0
(2 + 4i + (-3i + -6i2)) = 0

Combine like terms: 4i + -3i = 1i
(2 + 1i + -6i2) = 0

Solving
2 + 1i + -6i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
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 = {0.6666666667, -0.5}