(6+2i)(3+5i)=

Solution for (6+2i)(3+5i)= equation:

Simplifying
(6 + 2i)(3 + 5i) = 0

Multiply (6 + 2i) * (3 + 5i)
(6(3 + 5i) + 2i * (3 + 5i)) = 0
((3 * 6 + 5i * 6) + 2i * (3 + 5i)) = 0
((18 + 30i) + 2i * (3 + 5i)) = 0
(18 + 30i + (3 * 2i + 5i * 2i)) = 0
(18 + 30i + (6i + 10i2)) = 0

Combine like terms: 30i + 6i = 36i
(18 + 36i + 10i2) = 0

Solving
18 + 36i + 10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 18i + 5i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
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 = {-3, -0.6}