(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 = 19i
(3 + 19i + -14i2) = 0

Solving
3 + 19i + -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}