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

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

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

Multiply (3 + -5i) * (6 + 3i)
(3(6 + 3i) + -5i * (6 + 3i)) = 0
((6 * 3 + 3i * 3) + -5i * (6 + 3i)) = 0
((18 + 9i) + -5i * (6 + 3i)) = 0
(18 + 9i + (6 * -5i + 3i * -5i)) = 0
(18 + 9i + (-30i + -15i2)) = 0

Combine like terms: 9i + -30i = -21i
(18 + -21i + -15i2) = 0

Solving
18 + -21i + -15i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7i + -5i2) = 0

Factor a trinomial.
3((3 + -5i)(2 + i)) = 0

Ignore the factor 3.
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 '(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
Solution
i = {0.6, -2}