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

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

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

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

Combine like terms: 15i + 4i = 19i
(12 + 19i + 5i2) = 0

Solving
12 + 19i + 5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + i)(4 + 5i) = 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 '(4 + 5i)' equal to zero and attempt to solve:

Simplifying
4 + 5i = 0

Solving
4 + 5i = 0

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

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

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

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

Divide each side by '5'.
i = -0.8

Simplifying
i = -0.8
Solution
i = {-3, -0.8}