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

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

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

Reorder the terms:
(4 + 5i)(i + 4) = 0

Reorder the terms:
(4 + 5i)(4 + i) = 0

Multiply (4 + 5i) * (4 + i)
(4(4 + i) + 5i * (4 + i)) = 0
((4 * 4 + i * 4) + 5i * (4 + i)) = 0
((16 + 4i) + 5i * (4 + i)) = 0
(16 + 4i + (4 * 5i + i * 5i)) = 0
(16 + 4i + (20i + 5i2)) = 0

Combine like terms: 4i + 20i = 24i
(16 + 24i + 5i2) = 0

Solving
16 + 24i + 5i2 = 0

Solving for variable 'i'.

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

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

Simplifying
4 + i = 0

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

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

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

Simplifying
i = -4
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 = {-4, -0.8}