(4+5i)(6-i)=0

Solution for (4+5i)(6-i)=0 equation:

Simplifying
(4 + 5i)(6 + -1i) = 0

Multiply (4 + 5i) * (6 + -1i)
(4(6 + -1i) + 5i * (6 + -1i)) = 0
((6 * 4 + -1i * 4) + 5i * (6 + -1i)) = 0
((24 + -4i) + 5i * (6 + -1i)) = 0
(24 + -4i + (6 * 5i + -1i * 5i)) = 0
(24 + -4i + (30i + -5i2)) = 0

Combine like terms: -4i + 30i = 26i
(24 + 26i + -5i2) = 0

Solving
24 + 26i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -1i)(4 + 5i) = 0

Subproblem 1
Set the factor '(6 + -1i)' equal to zero and attempt to solve:

Simplifying
6 + -1i = 0

Solving
6 + -1i = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1i = 0 + -6
-1i = 0 + -6

Combine like terms: 0 + -6 = -6
-1i = -6

Divide each side by '-1'.
i = 6

Simplifying
i = 6
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 = {6, -0.8}