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

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

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

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

Combine like terms: 10i + 4i = 14i
(8 + 14i + 5i2) = 0

Solving
8 + 14i + 5i2 = 0

Solving for variable 'i'.

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

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 '(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 = {-2, -0.8}