(5+4i)(3+2i)=0

Solution for (5+4i)(3+2i)=0 equation:

Simplifying
(5 + 4i)(3 + 2i) = 0

Multiply (5 + 4i) * (3 + 2i)
(5(3 + 2i) + 4i * (3 + 2i)) = 0
((3 * 5 + 2i * 5) + 4i * (3 + 2i)) = 0
((15 + 10i) + 4i * (3 + 2i)) = 0
(15 + 10i + (3 * 4i + 2i * 4i)) = 0
(15 + 10i + (12i + 8i2)) = 0

Combine like terms: 10i + 12i = 22i
(15 + 22i + 8i2) = 0

Solving
15 + 22i + 8i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + 2i)(5 + 4i) = 0

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 '(5 + 4i)' equal to zero and attempt to solve:

Simplifying
5 + 4i = 0

Solving
5 + 4i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4i = 0 + -5
4i = 0 + -5

Combine like terms: 0 + -5 = -5
4i = -5

Divide each side by '4'.
i = -1.25

Simplifying
i = -1.25
Solution
i = {-1.5, -1.25}