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

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

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

Multiply (-3 + 7i) * (1 + -2i)
(-3(1 + -2i) + 7i * (1 + -2i)) = 0
((1 * -3 + -2i * -3) + 7i * (1 + -2i)) = 0
((-3 + 6i) + 7i * (1 + -2i)) = 0
(-3 + 6i + (1 * 7i + -2i * 7i)) = 0
(-3 + 6i + (7i + -14i2)) = 0

Combine like terms: 6i + 7i = 13i
(-3 + 13i + -14i2) = 0

Solving
-3 + 13i + -14i2 = 0

Solving for variable 'i'.

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

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

Simplifying
-1 + 2i = 0

Solving
-1 + 2i = 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 + 2i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2i = 0 + 1
2i = 0 + 1

Combine like terms: 0 + 1 = 1
2i = 1

Divide each side by '2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
Set the factor '(3 + -7i)' equal to zero and attempt to solve:

Simplifying
3 + -7i = 0

Solving
3 + -7i = 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 + -7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7i = 0 + -3
-7i = 0 + -3

Combine like terms: 0 + -3 = -3
-7i = -3

Divide each side by '-7'.
i = 0.4285714286

Simplifying
i = 0.4285714286
Solution
i = {0.5, 0.4285714286}