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

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

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

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

Combine like terms: 12i + 5i = 17i
(15 + 17i + 4i2) = 0

Solving
15 + 17i + 4i2 = 0

Solving for variable 'i'.

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

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

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
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 = {-3, -1.25}