(8+4i)(3+5i)=

Solution for (8+4i)(3+5i)= equation:

Simplifying
(8 + 4i)(3 + 5i) = 0

Multiply (8 + 4i) * (3 + 5i)
(8(3 + 5i) + 4i * (3 + 5i)) = 0
((3 * 8 + 5i * 8) + 4i * (3 + 5i)) = 0
((24 + 40i) + 4i * (3 + 5i)) = 0
(24 + 40i + (3 * 4i + 5i * 4i)) = 0
(24 + 40i + (12i + 20i2)) = 0

Combine like terms: 40i + 12i = 52i
(24 + 52i + 20i2) = 0

Solving
24 + 52i + 20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 13i + 5i2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + i)' equal to zero and attempt to solve:

Simplifying
2 + i = 0

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

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

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

Simplifying
i = -2
Subproblem 2
Set the factor '(3 + 5i)' equal to zero and attempt to solve:

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5i = 0 + -3
5i = 0 + -3

Combine like terms: 0 + -3 = -3
5i = -3

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {-2, -0.6}