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

Solution for (3+5i)(4-i)=0 equation:

Simplifying
(3 + 5i)(4 + -1i) = 0

Multiply (3 + 5i) * (4 + -1i)
(3(4 + -1i) + 5i * (4 + -1i)) = 0
((4 * 3 + -1i * 3) + 5i * (4 + -1i)) = 0
((12 + -3i) + 5i * (4 + -1i)) = 0
(12 + -3i + (4 * 5i + -1i * 5i)) = 0
(12 + -3i + (20i + -5i2)) = 0

Combine like terms: -3i + 20i = 17i
(12 + 17i + -5i2) = 0

Solving
12 + 17i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -1i)(3 + 5i) = 0

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

Simplifying
4 + -1i = 0

Solving
4 + -1i = 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 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

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

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5i = 0 + -3
5i = 0 + -3

Combine like terms: 0 + -3 = -3
5i = -3

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {4, -0.6}