(3+2i)(1+7i)=0

Solution for (3+2i)(1+7i)=0 equation:

Simplifying
(3 + 2i)(1 + 7i) = 0

Multiply (3 + 2i) * (1 + 7i)
(3(1 + 7i) + 2i * (1 + 7i)) = 0
((1 * 3 + 7i * 3) + 2i * (1 + 7i)) = 0
((3 + 21i) + 2i * (1 + 7i)) = 0
(3 + 21i + (1 * 2i + 7i * 2i)) = 0
(3 + 21i + (2i + 14i2)) = 0

Combine like terms: 21i + 2i = 23i
(3 + 23i + 14i2) = 0

Solving
3 + 23i + 14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + 2i)(1 + 7i) = 0

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

Simplifying
3 + 2i = 0

Solving
3 + 2i = 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 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Subproblem 2
Set the factor '(1 + 7i)' equal to zero and attempt to solve:

Simplifying
1 + 7i = 0

Solving
1 + 7i = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7i = 0 + -1
7i = 0 + -1

Combine like terms: 0 + -1 = -1
7i = -1

Divide each side by '7'.
i = -0.1428571429

Simplifying
i = -0.1428571429
Solution
i = {-1.5, -0.1428571429}