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

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

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

Multiply (5 + i) * (3 + 4i)
(5(3 + 4i) + i(3 + 4i)) = 0
((3 * 5 + 4i * 5) + i(3 + 4i)) = 0
((15 + 20i) + i(3 + 4i)) = 0
(15 + 20i + (3 * i + 4i * i)) = 0
(15 + 20i + (3i + 4i2)) = 0

Combine like terms: 20i + 3i = 23i
(15 + 23i + 4i2) = 0

Solving
15 + 23i + 4i2 = 0

Solving for variable 'i'.

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

Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve:

Simplifying
5 + i = 0

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

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

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

Simplifying
i = -5
Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {-5, -0.75}