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

Solution for (6+i)(3-5i)=0 equation:

Simplifying
(6 + i)(3 + -5i) = 0

Multiply (6 + i) * (3 + -5i)
(6(3 + -5i) + i(3 + -5i)) = 0
((3 * 6 + -5i * 6) + i(3 + -5i)) = 0
((18 + -30i) + i(3 + -5i)) = 0
(18 + -30i + (3 * i + -5i * i)) = 0
(18 + -30i + (3i + -5i2)) = 0

Combine like terms: -30i + 3i = -27i
(18 + -27i + -5i2) = 0

Solving
18 + -27i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -5i)(6 + i) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + i)' equal to zero and attempt to solve:

Simplifying
6 + i = 0

Solving
6 + i = 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 + i = 0 + -6

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

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

Simplifying
i = -6
Solution
i = {0.6, -6}